Compound interest is interest on interest. Each time it’s added, the balance grows, and the next round of interest is earned on the larger amount. Over a long time the effect is large.
Add a starting sum, monthly deposits and how often the interest is added, and you’ll see where the pot ends up.
How to use the Compound Interest Calculator#
- Enter your starting amount. Use what you have now, or zero if you’re starting from nothing.
- Add contributions and a rate. Enter what you’ll add each month and the yearly interest rate.
- Choose the time and compounding. Pick the years and how often interest is added.
The formulas#
P is the starting amount, r is the yearly rate as a decimal, n is the number of times interest is added per year and t is the time in years. 10,000 at 5 percent for 10 years, compounded monthly, grows to 10,000 × (1 + 0.05 ÷ 12)^120 = 16,470.09.
Here g is the growth factor over the whole period, i is the interest rate per month and C is the monthly deposit. With 200 a month added to the same 10,000, the pot grows to about 47,500 over the ten years, of which 34,000 is money you put in.
Why frequency matters less than time#
Compounding more often does help, but not by much. At 5 percent, yearly compounding gives an effective rate of 5.00 percent, monthly gives 5.12 percent and daily gives 5.13 percent. Doubling the time, or adding regular contributions, makes a far bigger difference. The effective annual rate is shown so you can compare accounts that compound differently.
Using the result sensibly#
The calculator assumes a fixed rate and deposits made at the end of each month. Real investments rise and fall, savings rates change and inflation reduces what money can buy, so treat the figure as an illustration. Compare with the APY calculator and the interest rate calculator.
A worked example#
Someone starts with ₦100,000, adds ₦20,000 every month and earns 12 percent a year, compounded monthly, for 10 years. They put in ₦2,500,000 in total. The future value is ₦4,930,812, so the interest earned is ₦2,430,812. The growth multiple is 1.97×. Most of the interest arrives late: in the last two years the balance grows by more than in the first five.
The effect of starting early#
Time has more effect than the rate or the amount. At 10 percent a year, ₦50,000 a month for 20 years grows to about ₦38 million. Waiting ten more years and then saving the same amount for 20 years from age 40 gives the same pot only at a much higher saving rate. The reason is that early contributions have more years to earn interest on their interest. If you cannot save much, start with a small amount and raise it each time you get a pay rise.
Rates, fees and inflation#
A quoted rate of 12 percent is a nominal rate. Compounded monthly it becomes an effective annual rate of 12.68 percent, which the calculator shows. Fees reduce the return, so a fund that charges 2 percent a year takes a large share of the growth over 20 years. Inflation reduces what the money can buy. If prices rise 15 percent a year and your savings earn 12 percent, the real value is shrinking. Use the APY calculator to compare accounts that compound differently.
Frequently asked questions#
Interest calculated on both your original amount and the interest already added.
Use A = P × (1 + r ÷ n)^(n × t), or enter your numbers above.
Monthly gives slightly more, but the difference is small compared with time and contributions.
No. It shows nominal growth only.
It is a shortcut: divide 72 by the annual percentage rate to estimate the years needed to double your money. At 8 percent, money doubles in about 9 years. The calculator shows the exact figure using your rate and compounding.
More frequent compounding gives slightly more interest, because interest is added to the balance sooner. At 10 percent a year, annual compounding gives an effective rate of 10 percent, monthly gives 10.47 percent and daily 10.52 percent. Time and rate matter far more than frequency, so choose the account with the better rate first.