Compound interest calculator

How the calculation works

Compound interest means you earn a return on your money and then on the return itself. Each period, the growth is added to the balance, so the next period's growth is calculated on a slightly bigger number. Over long stretches, that snowballing does more of the work than your deposits do.

This calculator works month by month. For each month it does two things:

1. Grows the balance. The balance is multiplied by one plus the monthly rate.
2. Adds your contribution. Your monthly amount is added at the end of the month, so it starts earning from the following month.

With monthly compounding, the monthly rate is simply the annual rate divided by 12. For other compounding choices, the calculator converts the annual rate into the monthly rate that gives exactly the same result: one plus the annual rate divided by the number of compounding periods, raised to (periods divided by 12), minus one. That keeps daily, monthly, quarterly and annual compounding comparable while you still add money every month.

For monthly compounding, the shortcut formula is:

• Starting amount part: starting amount times (1 + monthly rate) raised to the number of months
• Contributions part: monthly contribution times ((1 + monthly rate) raised to the number of months, minus 1), divided by the monthly rate

Add the two parts together and you get the final balance. The calculator's month by month loop gives the same answer and also lets it build the year by year table.

How to read your result

The headline is your balance at the end of the period. Under it:

• Total contributed is your starting amount plus every monthly deposit. This is money you put in yourself.
• Total growth is the final balance minus what you contributed. This is what compounding earned for you.
• The bars show how the final balance splits between your money and growth.

The table shows each year's ending balance and how much growth was added in that year alone. Watch the "Growth this year" column. It starts small and climbs every year, even though your deposits stay the same. That rising column is compounding at work.

A worked example

The calculator opens with $10,000 to start, $300 a month, a 7% annual return, 20 years, and monthly compounding. The monthly rate is 7% divided by 12, about 0.583%.

• The $10,000 on its own grows to about $40,387 after 240 months.
• The $300 monthly deposits grow to about $156,278.
• Together, the final balance is about $196,665.

You contributed $82,000 in total: the $10,000 start plus $300 times 240 months, which is $72,000. So growth accounts for about $114,665, or roughly 58% of the final balance.

Look at the table and you will see growth of about $841 in year 1 and about $13,126 in year 20. At the halfway point, after 10 years, the balance is about $72,022. The second decade adds far more than the first, because the base it grows on is so much larger.

Switch the compounding to annual and the balance comes out at about $190,958 instead. More frequent compounding helps a little, but the rate and the number of years matter far more.

Mistakes to avoid

• Expecting a smooth line. Investments rise and fall. A steady 7% every year is a simplification. Treat the result as an estimate of what an average return might do, not a promise.
• Ignoring fees. A yearly fund or account fee comes straight off your return. If you pay 1% in fees, enter a rate 1 point lower to see the effect.
• Forgetting inflation. A dollar in 20 years buys less than a dollar today. To see results in current dollars, subtract your expected inflation rate from the return you enter.
• Mixing up APR and APY. A savings account's APY already includes compounding. If you have an APY, choose annual compounding and enter the APY as the rate.
• Waiting to start. Because growth builds on itself, the early years carry the most weight. Shortening the time is usually costlier than lowering the monthly amount.

Common questions

What rate should I use?

For a savings account or certificate, use the rate the bank quotes. For investments, there is no fixed rate, so try a few cautious numbers and see how the result changes. Running a low, middle and high case gives you a range instead of a single guess.

Does compounding frequency make a big difference?

Less than most people think. In the example above, moving from annual to monthly compounding adds about $5,700 over 20 years. Changing the rate by one point or adding five more years makes a much bigger difference.

Are my contributions added at the start or end of each month?

At the end. Each deposit starts earning in the following month. If you contribute at the start of the month instead, your real result will be slightly higher than shown.

Does this include taxes?

No. Interest and investment gains may be taxed depending on the account type and where you live. For questions about tax-advantaged accounts or what you might owe, talk to an accountant or a financial adviser.