Compound interest calculator

With simple interest you earn interest only on the money you put in. With compound interest, the interest is added to the balance, and from then on it earns interest too. The longer the money stays invested, the larger the share of the final amount that comes from interest on earlier interest rather than from your deposits.

Three things decide the result: the rate, the time and how often interest is added (the compounding frequency). Time matters most. At a fixed rate, the growth in the last ten years of a 30-year period is far larger than in the first ten, because it is calculated on a bigger balance.

Interest rates are quoted per year. If a bank or a bond quotes 5% compounded monthly, it adds 5% ÷ 12 of the balance every month, which works out to slightly more than 5% over a full year. That full-year figure is the effective annual rate, also called the annual percentage yield (APY).

Starting amount only. Future value = P × (1 + r/n)^n×t, where P is the starting amount, r the yearly rate as a decimal (5% = 0.05), n the number of times interest is added per year (365 for daily, 12 for monthly, 4 for quarterly, 1 for yearly) and t the number of years.

Regular deposits. Each deposit grows from the day it is made. For a deposit D at the end of every month, the deposits are worth D × ((1 + i)^N − 1) ÷ i at the end, where i is the monthly rate and N the number of months. Deposits made at the start of each month earn one extra month of interest, so that result is multiplied by (1 + i).

Mixing frequencies. When interest is added on a different schedule from your deposits (for example daily interest and monthly deposits), the calculator converts the rate to the equivalent monthly rate, i = (1 + r/n)^n/12 − 1, and steps through the period month by month. This keeps the yearly growth exactly equal to the effective annual rate.

Simple interest. Future value = P × (1 + r × t). Interest is never added to the balance, so it never earns interest itself.

Effective annual rate. APY = (1 + r/n)ⁿ − 1. Inflation. The value in today's money = future value ÷ (1 + inflation)^t.

Take a starting amount of 10,000 at a yearly rate of 5% for 10 years, with no deposits. The table shows how the compounding frequency changes the result. These are illustrative round numbers, not a forecast of any real account or investment.

Now add a deposit of 200 at the end of every month, with monthly compounding. The 120 deposits total 24,000 and grow to 31,056.46; the starting amount grows to 16,470.09. The balance after 10 years is 47,526.55. Of that, 34,000 is money paid in and 13,526.55 is interest. If prices rise 3% a year over the same period, 47,526.55 in ten years buys about what 35,364.22 buys today.

The monthly interest on the starting amount in the first month is 10,000 × 0.05 ÷ 12 = 41.67. By the tenth year the balance is several times larger, so each month's interest is too.

Less than most people expect. In the example above, daily compounding beats yearly compounding by about 198 over ten years on 10,000, while the jump from simple interest to yearly compounding is about 1,289. A higher rate or a longer period changes the outcome far more than the compounding schedule. When you compare two savings products, compare their effective annual rates (APY), which already include the compounding.

A quick mental check is the rule of 72: divide 72 by the yearly rate to estimate how many years it takes to double your money. At 5% that gives 14.4 years. The exact figure at a 5% rate compounded monthly is about 13.9 years. The rule is an approximation that works best for rates between about 4% and 12%.

Regular deposits usually matter more than the starting amount over long periods. Deposits at the start of each month earn one more month of interest than deposits at the end, which adds a little to the result; switch the Timing box to see the difference.

To model money coming out, for example a monthly income drawn from savings, set Type to Withdrawal. If withdrawals are larger than the interest the balance earns, it shrinks every year; the table shows the year the money would run out at a constant rate. Real portfolios that pay an income also face changing returns, so a constant-rate calculation is only a starting point. If you hold dividend shares, our guide to dividend yield explains how the income from a stock is measured.

For a savings account or a deposit, use the APY or the stated rate and compounding the bank quotes. For government bonds, our US Treasury yields page shows today's yields from one month to 30 years, and central bank rates lists the policy rates that savings rates tend to follow. Why bond prices move when yields change is covered in bond yields and prices.

Stock market returns are not a fixed rate. An index such as the S&P 500 has risen in most years but fallen sharply in some, so a constant-rate calculation shows one smooth path, not what markets actually do. Inflation also eats into any rate; see inflation and stocks for how the two interact.

• The rate stays the same for the whole period. Real savings rates change, and investment returns vary from year to year.
• Taxes, account fees and fund charges are not deducted, so real results are lower.
• Deposits and withdrawals are the same amount every time; there is no yearly increase.
• Daily compounding uses 365 days a year. Some banks use 360 days, which gives a very slightly different result.
• Results are rounded to two decimals for display; the calculation itself is not rounded.