Compound interest calculator

How compound interest works

With compound interest, the interest you earn is added to your balance and then earns interest itself. The more often interest is added (compounded), the slightly faster the balance grows, though the difference between monthly and daily compounding is small.

A = P × (1 + r ÷ n)^{n × t}

• A is the final amount and P the starting amount.
• r is the yearly rate as a decimal (5% = 0.05).
• n is how many times a year interest is compounded (12 for monthly) and t is the number of years.

For continuous compounding the formula becomes A = P × e^{r × t}.

When you add monthly contributions, the calculator works month by month. It converts the yearly rate into the equivalent monthly growth rate for the compounding you chose, applies it, and adds your contribution at the start or end of the month.

Worked example

Put in 10,000 at 5% a year, compounded monthly, for 10 years, with no contributions:

A = 10,000 × (1 + 0.05 ÷ 12)¹²⁰ ≈ 16,470.09. Compounded once a year instead, it would be 16,288.95; compounded continuously, 16,487.21.

Add 200 at the end of every month and the balance after 10 years is about 47,526.55. You paid in 34,000 (10,000 + 120 × 200), so about 13,526.55 is interest. Paying the 200 at the start of each month instead gives about 47,655.95, because each contribution earns one extra month of interest.

Regular withdrawals: how long will the money last?

Fill in the withdrawal section to see money being drawn out, for example a retirement pot. The calculator still works month by month. In each month it takes the withdrawal (at the start or end of the month, or once a year in the first or last month of the year), adds interest on what is left, and stops paying out when the balance reaches zero. If the last withdrawal is bigger than the balance, only what is left is paid and the balance becomes zero: that is when the money runs out.

• Yearly increase raises the withdrawal once a year, from the second year of withdrawals, so it can keep pace with inflation: a 3% increase turns 10,000 into 10,300, then 10,609.
• Start year lets you save first and draw later. With "stop contributions" ticked, monthly contributions end in the year withdrawals begin.
• If the money is still there at the end of the years you entered, the calculator keeps going (up to 100 years in total) to tell you when it would run out at the same rates.

If the interest earned each year is more than you withdraw, the balance keeps growing and never runs out. If withdrawals are bigger, the balance shrinks, and it shrinks faster each year because there is less left to earn interest.

Worked example: withdrawals rising with inflation

Start with 250,000 at 5% a year, compounded monthly, and take out 10,000 at the start of each year, increasing by 3% a year.

• Year 1: 10,000 comes out first, leaving 240,000. A year's interest at 5% compounded monthly is 240,000 × ((1 + 0.05 ÷ 12)¹² − 1) ≈ 12,278.86, so the year ends at 252,278.86.
• Year 2's withdrawal is 10,300, year 3's is 10,609, and so on.
• After 30 years the balance is about 103,380.12, after paying out 475,754.16 in total. At the same rates the money runs out in year 35, when the 35th yearly withdrawal can only be partly paid.
• Taking 1,500 a month instead (18,000 a year, also rising 3% a year) uses the money up much sooner: it runs out in year 17, month 7.

The rule of 72

A quick mental check: divide 72 by the yearly rate to estimate how many years it takes money to double. At 5% that gives 14.4 years; the exact answer with yearly compounding is about 14.2 years. It is a rough guide and gets less accurate at high rates.

FAQ

What is the difference between APR and APY?

APR is the stated yearly rate before compounding. APY (or AER) includes the effect of compounding over a year. 5% compounded monthly is an APY of about 5.12%. If your bank quotes an APY, enter it with yearly compounding to get the same result.

Does this include inflation or tax?

Not on its own. The results are in today's money only if the rate you enter is already after inflation. For withdrawals, the yearly increase lets you raise the amount you take out in line with expected inflation. Tax on interest or gains is not deducted.

What is the "4% rule"?

It is a rule of thumb from US retirement research, best known from William Bengen's 1994 study of past US stock and bond returns. The idea: withdraw 4% of your savings in the first year of retirement, then increase that amount each year by inflation. In the historical periods he tested, a mix of stocks and bonds lasted at least 30 years. It is a description of the past, not a promise: results depend on the order of good and bad years, fees, taxes, your mix of investments and how long you need the money. You can try it here: for 250,000, enter 10,000 once a year rising with your inflation estimate. Remember this calculator assumes the same return every year, which real markets do not deliver.

Why does the money run out when the rate is higher than 4%?

If the withdrawal rises every year, it eventually overtakes the interest, even when the rate is higher than the starting withdrawal rate. From then on the balance falls, and less balance means less interest.

Can I use it for investments?

Only as an illustration. Investment returns go up and down from year to year; a steady rate is a simplification.

Estimates for planning only, not financial advice. Real returns vary, and fees and taxes reduce them.