On this page is an annual percentage rate to annual percentage yield or apr to apy calculator.

The bank will only quote an APR for many financial products, not the actual yield you'll pay if you go through with the loan or mortgage – the annual percentage yield (APY). This tool will let you convert an APR to an APY to compare to other yields or, alternatively, investment returns, fairly.

APR to APY Calculator

Using the APR to APY Calculator

You'll only need a couple of pieces of information to convert an APR to an APY, namely the APR you are quotes and the frequency. Here's what the tool needs:

  • Interest Rate/APR (%) - The APR you are quoted for the loan, mortgage, or other bank product.
  • Compounding Frequency - Choose how often the bank compounds interest on the product you are considering.

APR to APY Output

When you're happy, hit the "Compute APY" button to do the math. Here's what it outputs:

  • Annual Percentage Yield (APY) (%) - The equivalent annual percentage yield, or APY, using the assumptions you entered into the tool.

Comparing Like Quantities

APR and APY can be tricky, and the relationship between the two isn't easy to rectify in your head. Hopefully, this quick tool helped you out!

Here is a tool dedicated to the other direction and other tricky fixed income concepts in finance:

Below is a bank CD calculator, which lets you estimate how much interest you'll receive from a planned (or current!) CD investment. Enter a few details about your Certificate of Deposit and we'll let you know how much it will pay out when it matures.

Certificate of Deposit Calculator

Using the Bank CD Calculator

For the tool to estimate how much you'll get when the certificate of deposit matures, you have to fill out 4 fields:

  • Annual Interest Rate/APY (%) - Enter the Annual Percentage Yield (APY) advertised for your Certificate of Deposit. Rarely, you might be quoted an Annual Percentage Rate. Convert that to an APY and insert that number here.
  • Deposit Amount ($) - How much do you plan to invest in the Certificate of Deposit upfront?
  • Length of CD: - Enter the number of months or years for the CD to mature (you will enter the unit type/date type below).
  • CD Term Measured in - Choose whether the CD length is measure in years or months.

Certificate of Deposit Calculator Outputs

After you've successfully entered the terms of the Certificate of Deposit investment in the calculator, hit the "Compute CD Return" button. The tool will give you two outputs:

  • Final Balance ($) - When your Certificate of Deposit matures, our estimate of how much money you'll receive.
  • Interest Earnings ($) - Of the above final balance at maturity, this field shows which amount comes from investment gains on the CD.

Investing in the Future

While Certificates of Deposit aren't the most exciting investment in the world, they're an excellent tool for managing cash flow. When you absolutely need a certain amount on some date in the future, you can time a CD to mature right before, with an FDIC guarantee (in the United States, and up to a point) that the money will not disappear due to bank insolvency.

If you enjoyed this tool, enjoy some other investment calculators:

Below you'll find an investment calculator, where you can model the future growth of an investment you own (or are considering owning).

Enter details about the investment, your time-frame, and your planned future contributions to compute – and optionally graph and visualize – your investment. You can also optionally model your loss of purchasing power to inflation and taxes.

Investment Growth Calculator

Using the Investment Calculator

The nice thing about investments is – when they grow, anyway – your interest or unrealized capital gains compound. When you earn a return, it's based on the compounded balance you've made over time. Annual returns are quoted as a geometric average.

This tool loops through all of your planned future investments... or computes returns off a base balance.

Investment Calculator Inputs

To run the tool, first, enter some investment information and how you plan on adding to your balance in the future.

  • Current Balance: Enter the amount you currently have in the investment here (or '0' if this is a new investment).
  • Years to Invest: How many years you plan to hold – or optionally contribute to – an investment.
  • Contribution Amount: The amount you'll contribute every period you select below. If you only want to model growth, enter '0'.
  • Contribution Frequency: How often you will invest the above amount in the investment.

Additionally, you'll have to make some future projections. I know; these won't be perfect – but factoring in return and optionally a tax rate and inflation rate will better help you plan your future investments.

  • Investment Return Annually: The percentage return you expect this investment to make every year while you own it, on average.
  • Inflation: What percentage average annual inflation do you expect in the ensuing years? (To ignore, enter '0').
  • Tax Rate: When you withdraw the investment in the future, what marginal tax rate you expect to pay. (To ignore, enter '0').

Once you have those entered, the next section explains how to get a quick result, a graph, and even output your model to a spreadsheet program.

Investment Planning Tool Outputs

There are two modes: a simple, quick result at your total balance or an advanced investment visualization, which you can even choose to output.

Simple Investment Projection Calculation

To see the quick summary, click the blue 'Project Investment' button. You'll quickly see four summary statistics for your scenario:

  • Final Balance: In your scenario, the total amount you'd see before you choose to sell and pay taxes.
  • Post Inflation/Tax: The total amount you'd have based on paying tax on your gains and adjusting the remaining balance to account for inflation over time (essentially, inflation adjusting to today's dollars).
  • Market Gains: Of your final balance, how much came from returns since you were exposed to the market.
  • Your Contribution: The amount of your final balance that came from your periodic investments over time.
  • Market Gains: Our best guess at market gains over the remaining years in your career.

Advanced Investment Visualization (and Output)

While the summary statistics may be all you need, the tool will let you take it a step (or two) further and visualize your investment growth over time. If you instead select the orange 'Project & Graph' function, the tool graphs your balance at annual intervals and allows you to export the data.

Investment calculator default scenario showing effects of contribution, periodic investments, taxes, inflation, and growth

Note: Net balance is computed 'as-if' you sold and paid any taxes that year – consider it your theoretical balance if you stopped early. The final value does not factor in annual sales.

If you click the upper right 'hamburger' menu, you can export the scenario's investment data. Choose svg or png for graphics, or csv to further model in your favorite spreadsheet program.

Investment Calculator Methodology

As I noted in the 401(k) calculator, all projections are wrong... but some are useful. This tool models returns as a smooth graph up and to the right, compounded at the same frequency as whatever investment periodicity you choose.

That will never happen. And neither will you be able to predict the exact tax rate at some future date, nor inflation leading up until then.

Modeling an Uncertain Future in the Investment Calculator

Take the tool's output with a grain of salt – used right (and when you assume errors!), it can help you plan for what the future has in store.

It'll never be perfect. But it can certainly be useful, primarily when you use conservative inputs.

See some other useful tools which will help you decide what's possible (using historical data – not a guarantee of future returns, of course!):

Here you'll find a capital gains tax calculator, where you can model the cost to sell or hold on to an investment until you have favorable long-term capital gains.

Enter your investment information and tax treatment, and the tool will show you the difference between short and long-term capital gains – numerically and visually.

Capital Gains Tax Calculator

Using the Capital Gains Tax Calculator

In the United States, the IRS defines two types of capital gains for most investments (visit the link for details):

  • Short Term Capital Gains: Investments held for exactly one year or shorter
  • Long Term Capital Gains: Investments held for a year and a day or longer

Why bother holding longer? Favored tax treatment.

Federal taxes – and most states and localities which tax investments – give favored treatments for long term capital gains. These differing tax treatments are meant to bias investors towards longer holding periods by charging fewer taxes on these longer investments.

Capital Gains Tax Calculator Inputs

To run the tool, enter your investment and tax information:

  • Purchase Price/Cost Basis: Enter the amount you added to the investment, either at purchase or as your final cost basis.
  • Sale Price: What would the total value of the investment be at sale?
  • Commission: What commission or payment would you need to make to dispose of the asset.
  • Federal Marginal Tax Rate: What tax would you pay on a short term investment at the federal level.
  • Federal Long-Term Capital Gains Rate: What tax would you pay on a long term investment at the federal level.
  • State & Local Marginal Tax Rate: What tax would you pay on a short term investment at the state (and optionally, local) level.
  • State & Local Long-Term Capital Gains Rate: What tax would you pay on a long term investment at the state (and optionally, local) level.

When happy with your inputs, hit the blue 'Compute Capital Gains' button.

Capital Gains Tax Tool Tool Outputs

  • Capital Gain Type: The tool runs both "Short Term" and "Long Term" capital gains scenarios at once; follow the column to see details for a scenario.
  • Commission Paid: A reminder of the amount paid in commission to sell an asset.
  • Tax Owed: The total Federal (plus State and possibly Local) taxes owed to sell the asset.
  • Gain After Tax: The market gain remaining after you pay taxes on an asset sale.
  • Net After Sale: The total amount you'd realize if you liquidate the investment and pay commissions and taxes.

You'll also see a graph appear. On the left side, you'll see where the money goes in a short-term capital gains scenario. On the right, you'll see the same for long-term capital gains.

Capital gains calculator for default scenario showing taxes owed
Preview of the output for the default scenario.

On desktop, hover to see how individual components affect your final payout. On mobile or tablet, click the graph to see the components.

Additionally, you can export the data using the 'hamburger' menu in the upper right. Export to a chart by selecting 'svg' or 'png'. Alternatively, export to 'csv' to play with the data in your favorite spreadsheet program.

See Tax Treatment in the Capital Gains Tax Calculator

You shouldn't let tax considerations completely control your investment strategy – but you need to recognize taxes make a huge difference in your gains. Sometimes waiting a short period for long term capital gain treatment is worth the risk of staying in the market.

Now: that's not investment advice. Even one day can theoretically tank an investment, of course. You do need to consider risk vs. reward, and sometimes LTCG suggests you roll the dice.

Here are some investment calculators to get a feel for investment returns:

On this page is a 401(k) calculator, also useful for modeling a 403(b).

Enter details of your current balance, age, salary, and retirement plan plus your employer's details, and the tool will model (or graph) your future savings.

401(k) or 403(b) Planning Calculator

Using the 401(k) Calculator

401(k) plan (or a 403(b) plan for non-profits) is one of the most popular perks employers offer. It is named after a provision in the US tax code – yes, even in other countries that name their plan "a 401(k)".

In a traditional plan, you contribute tax-free dollars today to pay taxes on the back-end – a fantastic perk if you plan to withdraw less income in retirement. Many employers also offer a Roth version, where the Government promises never to tax you again on the money you contribute today – after paying the appropriate tax.

Also, in many cases, your employer might contribute a match. If you put up a certain amount from your paycheck, your employer might sweeten the pot by contributing a proportionate amount.

Planning Tool Inputs

Deferred plans have many complications. To use the 401(k) tool, you'll have to gather some data about your plan:

Current 401(k) Plan Inputs

  • Current 401(k) Balance: If you currently have some money in your 401(k) or 403(b), enter the amount here.
  • Annual Salary: The amount you make a year.
  • Percentage Contribution: What percentage of your salary will you contribute to the plan.
  • Current Age: Your age today.
  • Retirement Age: The age when you plan to retire.
  • Employer Match: What percentage of your whole dollar salary will your employer match? (For many companies, this is 25%, 50%, 100%, or 200% on the dollar you contribute).
  • Up to What % of Salary?: What is the maximum salary percentage where the plan applies?

Market and Raise Assumptions

All projections are wrong – but some are useful.

Unfortunately, you'll need to do some prognosticating here. We'll need a guess at how your salary will evolve, as well as an investment of how your investments will perform.

Tool Outputs

You can either see summary statistics modeling your 401(k) or 403(b) or increase the resolution and graph your projections.

Simple 401(k) Calculation

To see the summary, click the blue 'Project 401(k) Balance' button. You'll then see the total amount, plus a breakdown of the funding sources.

  • Balance at Retirement: Our best estimate of the total balance in your 401(k) when you retire.
  • Starting Balance: The amount of money you started the projection using (you told us right above).
  • Your Contribution: Total contribution over the remainder of your career.
  • Employer Contribution: Match contribution for the remaining years in your career.
  • Market Gains: Our best guess at market gains over the remaining years in your career.

Advanced Calculation

While the summary statistics are fun, sometimes you really just need to see a 401(k) balance visualization.

If you hit the orange 'Project & Draw Graph' button, you'll get all the information from the simple calculation plus a graph which shows the annual change. If you hover (click/tap on mobile), you can see the 'total' balance at the end of each year, plus how the buckets have evolved to that point.

401(k) Growth Calculator Model for Base Scenario

If you click the upper right 'hamburger' menu, you can export the graph's projection data. Choose svg or png for a graphical export, or use the csv option to model in your favorite spreadsheet program.

401(k) Calculator Methodology

Necessarily, I had to make a few simplifications in the tool – it's impossible to see the future, as you know.

I've already mentioned that you need to add your projections for your income, plus stock returns. Additionally, the tool will compound returns monthly, assuming that stock has a smooth and clean return (it never does!). The tool currently doesn't 'cap' input; it can model contributions larger than the 401(k) contribution limit.

Finally, the tool assumes a whole 'age,' with you retiring at the end of your Retirement Age. If you select a retirement age of 65, the tool assumes you receive 12 months' worth of paychecks as a 65-year-old. Also note, the average retirement age in the US is a bit lower than 65.

401(k)s and 403(b)s: Popular Company Benefits

401(k)s and 403(b)s are popular for a reason. They let you adapt your retirement strategy to changing tax regimes – by giving up liquidity, you gain substantial planning benefits long term.

See some other useful tools which will help your planning:

On this page is an employee stock purchase plan or ESPP calculator. The tool will estimate how much tax you'll pay plus your total return on an ESPP investment under three scenarios:

  • Holding Period not met, short term capital gains
  • Holding Period not met, long term capital gains
  • Holding period met

Employee Stock Purchase Plan Calculator

Using the ESPP Tax and Return Calculator

An ESPP – or Employee Stock Purchase Plan – is an employer perk that allows employees to purchase a company's stock at a discount.

Qualified ESPPs, known as Qualified Section 423 Plans (to match the tax code), have to follow IRS rules to receive favored treatment. The most significant implication for employees is a $25,000 benefit cap.

In the most common setup, employees set aside income (usually at a max of 10 or 15%) over six months. They receive a discount of up to 15% on either the market value at the grant date or execution date.

Of course, company plans and situations vary quite a bit. Hopefully, this tool helps make sense of things.

Employee Stock Purchase Plan Tool Inputs

Employee Stock Purchase Plans have many complications. To use the ESPP tool, you'll have to gather some data about your plan:

Company ESPP Inputs

  • Grant Date Share FMV: The fair market value of the ESPP shares when your company extends the option to buy them.
  • Exercise Date Share FMV: The fair market value of the ESPP shares when they exercise.
  • Discount vs. Price (Hit the toggle to flip)
    • ESPP Discount (%): If your plan is a percentage discount off the lower price at exercise or grant, enter the percentage here.
    • Price Paid per Share ($): If your plan has a different discount mechanism, enter the price you pay per share. (Also useful if you already know what you paid).
  • Shares Bought: Shares bought in this ESPP cycle. Note – the tool will model selling every share you enter here.
  • Share Sale Price: The price per share at the time of sale.
  • Commission: If you paid (or will pay) a commission to sell, enter it here.

Tax Inputs

To calculate the difference in return between holding periods, you need to enter various tax rates.

  • Marginal Tax Rate: Enter your marginal tax rate – that is, for each additional dollar you earn, what percentage goes to tax. Be sure to add Federal, State, and Local tax rates, if applicable.
  • Short Term Capital Gains Tax Rate: Enter your short term capital gain rate. For many states (and localities), this is equal to the marginal income tax rate.
  • Long Term Capital Gains Tax Rate: Enter your long term capital gain tax rate. Again, if applicable, add any state or local taxes.

ESPP Tax and Return Tool Outputs

Depending on how much information you need, the tool has a simplified mode and an advanced mode

The simplified ESPP mode will only show your cost basis, the total tax you owe, plus your gain or loss. The advanced mode will break down income and capital gains and show the various types of tax you'll pay.

For both computations, three major buckets have a significant effect on taxes. The ESPP gives you an option to purchase company shares at a discount – but depending on your holding period, the amount the IRS lets you allocate to capital gains and income will change.

See the sections below for more details about the Disposition and Capital Gains matrix.

Simple Calculation

To use the basic tool, click the blue 'Compute ESPP Return and Tax' button.

  • Disposition/Capital Gains: Under the corresponding column, you'll see the tax owed and total gain for that holding period and capital gain scenario.
  • Cost Basis: Your cost to purchase the shares.
  • Total Tax: The tax owed for this scenario.
  • Net Gain: Both the dollar gain plus the percentage return on investment for the ESPP investment. (To compute an annualized return, use the CAGR calculator).

Advanced Calculation

To use the advanced tool, click the orange 'Compute & Show Breakdown' button.

  • Disposition/Capital Gains: As with the basic calculation, you'll see columns for the disposition and capital gains treatment matrix.
  • Ordinary Income: Based on your holding period, the amount of income you recognize when you sell the shares.
  • Capital Gains: Again, based on the holding period, this shows the amount of capital gains you realize when selling the shares.
  • Income Tax: The amount of income tax you will owe for the three combinations of holding periods and capital gains treatment.
  • Capital Gains: Based on your capital gains treatment, the amount you will owe in capital gains taxes.
  • Net Gain: The absolute dollar gain plus the percentage ROI on your ESPP investment.

ESPP Holding Period and Capital Gains Treatment

As you can see in the tool, three major categories determine your final gain on an ESPP investment. I call them:

  • Disqualifying/STCG for Disqualifying Disposition, Short Term Capital Gains
  • Disqualifying/LTCG for Disqualifying Disposition, Long Term Capital Gains
  • Qualifying/STCG for Qualifying Disposition, Short Term Capital Gains

Here's how the two labels interact.

ESPP Capital Gains Treatment

The capital gains treatment is straightforward – it's defined by the IRS (and matched by most states and localities). In general:

  • If you hold an investment for more than one year, it's a Long Term Capital Gain.
  • If you hold an investment for under a year, it's a Short Term Capital Gain.

The clock starts ticking when the option is exercised – when you receive the ESPP shares. If you hold the shares for longer than a year, you get to pay the advantaged rate – even if you don't meet the terms for a qualifying disposition.

See more about capital gains taxes in DQYDJ's calculator.

ESPP Holding Period – and Disposition

Whether your ESPP investment qualifies for superior treatment on the holding period side also boils down to guidance from the IRS.

For a Qualifying Disposition in §423 employee stock purchase plans, you need to hit two benchmarks:

  • You must hold the shares for 1 year after you receive them (the same as for capital gain treatment, above)
  • You must hold the shares for 2 years after the option was granted (which is often 6 months before you receive the shares)

If you don't meet both benchmarks and sell early, it is a Disqualifying Disposition.

Why bother holding longer?

  • Qualifying Disposition: Income is the difference between the lower of the fair market value at the grant date or sale date and the price you paid. (With a minimum of $0). However, there is no provision for the exercise price – this can cause you to owe more income taxes than you'd otherwise expect in certain scenarios.
  • Disqualifying Disposition: Income is the difference between the fair market value at the execution date and the price you paid.

Qualifying dispositions can be quite a good bonus – especially when your share price takes off during the offering period! And with either disposition, you don't recognize income until you sell your shares.

ESPP: An Excellent Corporate Perk

Your stock purchase plan is an excellent benefit.

None of this is investment advice. But: except in the exceptional circumstance that your company goes bankrupt, it's nearly a no-lose scenario. By giving up liquidity for a specific holding period, you get a large gain on the back-end.

And while you certainly should heavily weight selling right away and diversifying your investments – it's complicated. By holding your ESPP shares longer, you can defer income until it's more advantageous to recognize it (perhaps after moving out of a high tax state?).

In the mood for other investment calculators? Try these:

Dollar Cost Averaging is a set it and forget it investment strategy that lines up well with how your paycheck works. You're paid on a periodic basis, and if you use DCA... you turn right around and invest on a periodic basis too.

Today I'll talk about what dollar cost averaging is, how you should use it, and answer the burning question: does dollar cost averaging work?

What is Dollar Cost Averaging?

Dollar Cost Averaging is a strategy where you invest money into the same investments on a regular basis. You make those purchases without even looking at the price – again, dollar cost averaging is a set it and forget it investing strategy.

Investments rise and fall in value all the time. This means that you'll buy more of an investment while the price is low and less while the price is high.

On average, though, using DCA you'll get a middling price – which tends to increase over time.

Meme guy plus an arrow and the word "stonks" which is stocks

Benefits of Dollar Cost Averaging

There are quite a few benefits of dollar cost averaging, even beyond your investment in the stock market.

Here are a few benefits of dollar cost averaging:

  • Reduces cognitive load: Most of you – even if you work in finance – have better things to do than pick stocks every 2 weeks.

    Dollar cost averaging lets you set an investment up front and automate it. Then you only need to look at your plan at a scheduled time annually.
  • Avoids timing the market: Even if you are a very good investor, it's extremely hard (and others will say impossible) to time the market.

    Dollar Cost Averaging just plows ahead mechanically no matter the market conditions. You'll win some and you'll lose some, but it'll all average out over time.
  • Removes emotions from investing: If your money is on autopilot through a dollar cost averaging plan, you don't have to worry about your emotions getting in the way of making investments.

    You know you should invest, but it can be hard when you're fearful. If your DCA plan is still running, you don't have to worry – you'll buy the lows, highs, and everything in between.

Are There Drawbacks to Dollar Cost Averaging?

Alas, there are some downsides to dollar cost averaging. But: they are mostly avoidable (with the possible exception of management costs inside your 401(k))

Let's look at how to avoid dollar cost averaging pitfalls.

Avoid Costs when Dollar Cost Averaging

The first trap in dollar cost averaging is cost. Costs mainly appear through transaction costs or investment costs (such as management fees).

When you buy stocks or ETFs through most brokerage accounts, you have to pay a commission.

Commissions vary per brokerage, but assume for most brokerages it's somewhere between $5 and $100. It depends on factors such as whether you buy online or dial into a company to trade.

Those fees up quickly - especially if you average into multiple stocks or ETFs. And if you purchase mutual funds they might have a load which acts much like a commission.

You also have to watch for management fees.

ETFs and mutual funds come with management costs, and not all funds are created equal. You should look for low cost, no-load mutual funds and ETFs for your DCA plan. And if you only have high cost funds inside your 401(k), you need to appeal to your company to add better options.

Bottom Line: Dollar Cost Averaging is easiest with a no-load mutual fund. Alternatively for ETFs and stocks, look for a broker that has free trades. (Or invest in stocks which have free "Direct Reinvestment Plans" – also called DRIP plans).

Avoid Underperforming Versus Lump Sum Investing

I wrote about how lump sum investing is better for a windfall. That post holds up – if you receive a lump sum, you should generally invest it all at once.

However, there is negative benefit to saving up in order to invest a lump sum. The positive drift of the stock market works against you if you're out of the market.

Bottom Line: Unless you have foresight the market is about to drop, you will lose if you save your paychecks to make a later lump sum purchase.

How to Dollar Cost Average

Convinced that dollar cost averaging is the right everyday (well... every two week?) investment strategy?

Good – it's simple to get things going:

  1. Set your target asset allocation for your DCA funds (for example, 80% stock 20% bonds)
    • Revisit this on a periodic basis; perhaps once a year. Resist the urge to change too often.
  2. Apply your allocation across all your accounts where you DCA
    • For example, set your allocation across your 401(k) and an IRA
  3. Automatically send money to your accounts
    • For some accounts (such as your 401(k)) you can push money automatically. For other accounts such as an IRA or 529, you might need to deposit your paycheck in a bank account first then pull money.
  4. That's it. Go back to step 1 once a year or so.
Set up your dollar cost averaging. Evaluate once a year. Profit 📈

Does Dollar Cost Averaging Work?

The subtext here is: "will I make money from dollar cost averaging?".

And the answer? Almost certainly, yes. Dollar cost averaging works over time.

The few scenarios where the answer is no involve population collapse, famine, war and other societal issues. In these pessimistic situations you have bigger problems than your retirement portfolio, however.

So, back to yes.

You're on Don't Quit Your Day Job... I'll prove it to you.

These next few calculators have periodic investing features. Using your own choice of inputs, you can see the effect of continuous investments into something:

*We don't – yet – have a mutual fund return calculator

Please use a long enough time period in your scenario. Dollar Cost Averaging is a strategy you employ over a career, not a few paychecks.

Dollar Cost Averaging Worked in the United States. What About Japan?

It's true – Japan's stock markets have been range-bound for a ridiculously long time. And since World War II Japan has had a relatively strong economy and avoided wars.

However, the stock market hasn't collapsed entirely. It's just that Nikkei lump sum investments in the 1980s have failed to keep up with inflation.

If you started your career in Japan in the late 1980s and continued to periodically invest, you would have also invested after the fall. You didn't perform as well as investors in the United States, but dollar cost averaging is viable even in Japan.

In Conclusion: You Should Dollar Cost Average Where You Can

You probably see a fair number of lump sums annually.

RSUs, ESPPs, bonuses, tax returns, asset sales, and (sadly) inheritances will all leave you with windfalls and require a different investment strategy.

But for your own peace of mind, the majority of your investing should be automatic. Wherever possible, plan your investing once a year – in advance – and put it on autopilot using dollar cost averaging.

And I'm not a hypocrite here.

I max my 401(k) annually, and time it to finish in December (to catch the full match). I send funds to my daughters' 529s twice a month, and once a month send money to a brokerage and a couple roboadvisor accounts.

I'd rather talk about efficiency here with you all than worry about where to put my money every two weeks. Even if DCA doesn't cover my entire investing strategy.

And don't you enjoy our time together? Let me know how you employ dollar cost averaging in the comments.

Dollar Cost Averaging (DCA) is oft-touted as the savior for all of investing's problems. Reality, on the other hand, is a bit different – in this post we'll show why lump sum investing usually beats dollar cost averaging when you have both options.

We'll use the S&P 500 in the United States as an example. (Skip ahead if you want to see math the typical difference between lump sum and dollar cost averaging.)

What is dollar cost averaging?

Dollar Cost Averaging (or DCA) is a style of investing where you automatically invest money on a regular interval. You buy more shares when prices are low, and fewer shares when prices are high. In essence, you bet on the average – hopefully DCA prevents you from terrible purchase times.

As a bonus, dollar cost averaging fits the general schedule of how people normally get paid. For example every two weeks you might get your paycheck, and also automatically invest in your 401(k). This is our suggested style of investing on a regular basis.

What is lump sum investing?

Lump sum investing is a style of investing where you have a large amount of money and you invest it all at once. Unlike dollar cost averaging, you don't slowly wade into the market... you make a big splash.

Lump sum investing is generally not applicable to your paycheck, whether it's weekly, bi-monthly, or some other regular schedule. It's more applicable to a windfall, which might include:

  • Annual bonus
  • Sale of equity (that you want to redeploy)
  • Inheritance
  • Tax return
  • Sale of a house
  • Sale of a business
  • Any other one-off, non-repeatable money you receive

When is dollar cost averaging or lump sum investing better?

Dollar cost averaging is on average inferior to lump sum investing... when both options are available. That means if you have a large sum of money to invest, it's better to invest immediately than to slowly drip it into investments.

Usually, these large sums are called windfalls: large influxes of money you are prepared to invest. They might be from something in that above list or some other source. Whichever way, you now have a large amount of cash you'd like to invest.

When you have extra funds, you usually shouldn't tiptoe into the market. Instead, you should dive right in with a lump sum investment. 

Don't believe me? The rest of the post will show you the math.

Lump Sum Investment Caveats

Mathematically, lump sum investing wins more than it loses... but sometimes it's more important to hedge the risk of a fall than to maximize your expected value.

But if you're younger, have more risk tolerance, or otherwise have a long time horizon – this tilts the game even more in lump sum's favor. Still: your situation may be similar, but remember you are unique

Always consult a financial planner if you have doubts about implementing any investment strategy. This is not advice, and of course, past performance does not guarantee future results

Calculating The Real Return on the S&P 500

We're using the S&P 500 index, a basket of 500 domestic stocks, as a representation of the total stock market in America. There are other options, but it is a commonly used proxy for the 'market' in the United States.

S&P 500 Total Return vs. Index Price Return to illustrate dollar cost averaging and reinvesting
S&P 500 Total Return vs. Index Price Return (1988-2019) S&P Dow Jones Indices

Above you can see a chart of the real price (in orange) that the S&P 500 closed at on the dates listed on the x-axis. The chart covers the period from mid-1989 to mid-2019. 

In blue is the total return price, a made up value which includes the effects of dividends paid and reinvested. This reflects the (estimated) real return of the index, if you held the component stocks and reinvested dividends. 

Using our S&P 500 total return calculator, you can see during the period from June 1988 - July 2019 the S&P 500 returned around 8% index level, and over 10% with dividends reinvested. The gap seems small, but that's the difference between 1000% and 2000% returns in that time-frame!

So, as you can see we need to take dividend reinvestment into consideration in this math.

Stock Return Drift Rate

It's true – past performance is no guarantee of future results. However, history does suggest that American stocks tend to increase. Your results may vary... for example look at recent history in Japan.

We like to call the bias for stock to move up and to the right the drift rate.

What is drift rate?

Drift rate or drift velocity is a borrowed term from physics and refers to the average velocity of charged particles – often electrons – in an electric field.

Electrons actually move in all directions, but when you have potential (voltage), electrons tend to move in the same direction. We look at stocks (or at least indexes) the same way: even though they move in all directions on a day, they tend to move up and to the right over time.

What is the daily drift rate of stocks?

On any average day since January 1871, US stocks have increased about .0239%. (Including non-market days and weekends, ignoring inflation adjustments)

Here's how we get that number:

  • Use the S&P 500 Calculator from January 1871 to July 2019
  • Grab the "Total S&P 500 Return" number: around 41,150,450% total return
  • Calculate the number of days for 148.5 years: about 54,210 days
  • Figure out the drift rate is ~ .0239% a day ( or ~9.09% a year)

Again, historic performance doesn't guarantee anything about the future. But: there has hitorically been minor upward pressure on US stock in aggregate.

Call it around .02-.025% daily.

Comparing Dollar Cost Averaging and Lump Sum Investing

Now that we have all the ingredients, let's finally put dollar cost averaging and lump sum investing head to head.

We'll assume a windfall of $10,000, and either invest it on the first day of the year or invest $192.31 every 7 days:

Lump Sum vs. Dollar Cost Average in a smoothed scenario on the historic S&P 500.
Smoothed DCA vs. Lump Sum investments of $10,000 over one year versus historic S&P 500

And there you have it – at historical average S&P 500 performance and weekly DCA, the dollar cost averaging strategy is $451.25 less after a year. That's essentially an annual insurance cost of 4.14% off the total potential.

Choosing the Right Investment Strategy

Obviously, this isn't a perfect simulation. Off our heads, it's missing:

  • Inflation
  • Interest on the DCA money held in cash while waiting to invest
  • Taxes
  • A lot more...

However, you can see that the normal drift rate of stock means lump sum investing is better when you have the option.

Dollar cost averaging matches well with your paycheck. For deploying a windfall, though, it will typically look like very expensive insurance.

That doesn't mean it's not worth it!

Perhaps you can sense – or are very fearful – the stock market will drop in the near future. Maybe it's psychologically easier for you to drip funds into investments than to throw everything in at once.

And sometimes in retrospect, DCA will come out on top when both options were available. However, the burden is on dollar cost averaging to prove it; the historical default – at least in the United States and most major economies – should be to prefer lump sum investments.

For more details in the real world, you can use our historical investment calculator on the S&P 500.

Enter a monthly average or set a large up-front value for an investment. You'll see that for a majority of time-frames, lump sum is better... but you can certainly find exceptions.

Takeaway: Lump Sum Usually Beats Dollar cost Averaging

Unless you have good reasons to believe there will be a market fall, or DCA is the only way for you to invest due to psychology... you should bias towards lump sum investing.

Have fun out there, and no matter which style you choose may your portfolio value always move up and to the right!

On this page is a detailed compound interest calculator, along with the compound interest formula and examples.

The calculator allows you to calculate compound interest from a starting lump sum, periodic additions, and for annual, monthly, and daily compounding periods. The calculator also graphs the growth of the investment over time and report a final amount.

Compound Interest Calculator

Using the Compound Interest Calculator

  • Investment Starting Amount - The lump sum at the beginning of the compounding period. If you are modeling your portfolio, use "today's value".
  • Periodic Investment Amount - The amount, in dollars, you add on a periodic basis.
  • Periodic Addition Frequency - How often you add that amount to your portfolio.
  • Interest Rate - The annual percentage rate the investment pays every year (quoted as APR if it is a bank account or similar)
  • Periods to Compound - The number of periods of the below type that the deposit and additions will compound.
  • Type of Periods - How often interest is applied. This field also affects the number of periods field set above (e.g. if you select 'Daily', make sure you enter the number of days to compound).

Compound Interest and Your Portfolio

Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.

Albert Einstein

Compound interest is a powerful concept fully worth grasping while learning more about your investment portfolio. At its heart: the money in your account earns interest, but the interest itself also earns interest.

In a sense: the money your money earned eventually snowballs into a larger and larger base on which you earn further interest.

The exact same concept applies when discussing dividends. Over a 40 year career, dividends and interest paid on previous dividend-reinvested shares can make up the majority of your portfolio.

The Compound Interest Formula

The compound interest formula is:

P(1+\frac{i}{n})^{nt}

Where:

  • P is the principal, or starting amount
  • i is the interest rate, APR
  • n is how many times per year the sum is compounded
  • t is the number of years to run the calculation

Let's work through a scenario now using the compound interest calculator and the compound interest formula:

Starting with $1,000, how much money would you have if you put your money into a savings account with: a 5.5% APR, compounded daily, for 5 years?

A naive calculation would say: $1,000 * 5.5% = $55 a year, multiply that by 5 and you get $275 for a total of $1,275 after 5 years.

That's incorrect, however. Plugging the numbers into the calculator, you get $1,316.50.

Plugging the numbers in the compound interest formula, we get:

1000 * (1 + (.055 / 365) ) ^ (365 * 5) =

1000 * (1 + (.0015068...) ) ^ (1,825) = 1000 * 1.3165034... =

$1,316.50

And there you go: without a feel for compound interest, somebody could spirit away $41.50 with you none the wiser!

The Effect of Compounding Frequency on Interest

One of the variables we noted in the compound interest calculation was the idea of compounding frequency

Think of compounding frequency as how often the compounding works on itself (compounding on compounding - it's all compounding all the way down!). 

Daily compounding means the rate is applied to the balance at the end of every day. Likewise for other forms of compounding: weekly, monthly or annual. 

There is also the idea of continuous compounding, where the compounding is always happening on an instantaneous sum of money.

The best way to get a sense of how the different compounding period affect the balance in an account is on a graph:

Compound interest calculator: the effect of compounding periods
(Wikipedia user Jelson25(

As you can see, compound interest is a simple topic with some complicated details. 

In the end it boils down to one simple fact: interest works upon previous interest. Whether this helps you or hurt you depends on what side of the transaction you are.

Heed Albert Einsteins advice, understand compound interest, and profit from it as much as you can.

For some other calculators and articles in our investment basics series, please try:

On this page is a present value calculator, sometimes abbreviated as a PV Calculator. Present value is an estimate of the current sum needed to equal some future target amount to account for various risks. Using the present value formula (or a tool like ours), you can model the value of future money.

Using the Present Value Calculator

  • Future Amount – The amount you'll either receive or would like to have at the end of the period
  • Interest Rate Per Year (Discount Rate) – The annual percentage rate investment return you'd earn over the period of your investment
  • Number of Years – The total number of years until the future sum is received, or the total number of years until you need a future sum. (You can enter fractional years, such as 6.5)
  • Present Value ($) – The amount the future sum is worth today with the assumptions in the input fields

The Present Value Formula

The general solution comes in this formula:

Present value formula for the calculator
The present value formula for annual (or any period, really) interest.
PV=\frac{C}{(1+i)^n}

where:

  • C = Future sum
  • i = Interest rate (where '1' is 100%)
  • n= number of periods

Example Using the Present Value Formula

In the simplest case, let's say you're an excellent investor and can get a 10% return on your money. You have $100 today, and you stay invested for three years:

Start:    $100
Year 1:  $110
2:  $121
3:  $133.10

If I asked you for $100 today, promising to give you $120 at year three... I'd hope you'd turn that down. The present value of $120 in three years, if you have alternatives that earn 10%, is actually $90.16.

That is to say, the present value of $120 if your time-frame is 3 years and your discount rate is 10% is $90.16.

For the above problem, your sum would be $133.10. Here's how the math works out:

Inputs: $133.10 in 3 years given 10% investment returns

PV = 133.10 / (1+.1)^3

= 133.10 / 1.1^3

= 133.10 / 1.331

PV = $100.00

and for my generous offer of $120:

Inputs: $120.00 in 3 years given you could get 10% investment returns elsewhere

PV = 120 / (1+.1)^3 = $90.16

I hope you'd agree now. If you can make 10% a year you should turn down my offer of $120 in three years for $100 today.

Why is present value important?

Future quantities deal with both inflationary (or deflationary) pressures, opportunity costs, and other risks to the value of your final sum. The actual equivalent value of a sum in the future is (almost) never the same amount as having a lump sum today.

That's where 'Present Value' comes into play.

If you have a return estimate for what you could earn with a lump sum investment today, you can easily estimate what that future value is worth. Alternatively, present value also tells you the amount you would need to invest today if you needed to end up with the final lump sum assuming a given return... just know that forecasting of this sort is never better than an educated guess!

Using the Present Value Formula and Calculator to Value Investments and Tradeoffs

While we're insinuating that 10% is an unreasonable discount rate, there will always be tradeoffs when you're dealing with uncertainty and sums in the future.

For a real-life investment measure, take a look at our Dow Jones Return Calculator.

After dividends and inflation are factored in, you would have seen about a 10% return, ignoring taxes and fees, since the Dow Jones Industrial Average has existed. (Remember, only adjust for inflation if you also adjust the final amount for inflation as well!) We're not sure if that's an accurate return estimate going forward, so please form your own estimate.

Regardless of your number, when you forego money today, you're giving something up in the future. That's true even if you're only able to make 1% on your money reliably.

And, yes, sometimes it's possible that a return of capital may be more important than a return on capital. In that sort of scenario money in the future would be worth more than today.

When should you use present value estimates?

Present value estimates are useful for evaluating job offers.

DQYDJ

Other than while evaluating investments, present value estimates are useful for evaluating job offers.

Many of you readers are in industries which have some sort of equity or variable compensation in your annual income. Any honest accounting of an offer evaluates your compensation other than salary, such as stock, options, or bonuses with some sort of a present value calculation (Total Compensation).

Bonuses are first to go in a recession, options can go to zero (especially in early stage companies) and stock can go up, down.. or even to zero.

Future values are actually a range of possible values... some of them zero. 

Every dollar of current salary is more valuable than variable compensation... although it doesn't have the upside of variable pay, it is safer than other income forms. When using the present value calculator you can adjust for that uncertainty by reducing the amount of future value and running the numbers again.

We hope you enjoyed this brief look at evaluating investments using the present value formula. Keep this concept in mind whenever you evaluate your options going forward.

What other calculators do you have?

Try our other financial basics and valuation calculators:

See all our financial calculators here.

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DQYDJ may be compensated by our partners if you make purchases through links. See our disclosures page. As an Amazon Associate we earn from qualifying purchases.
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