Compound interest formula: yearly, quarterly, monthly and daily

The compound interest formula is A = P × (1 + r/n)^n×t. Interest is added to the balance and then earns interest itself. This page shows how the number of times interest is added each year (n) changes the result, and why it matters less than the rate and the time.

The formula

A = P × (1 + r ÷ n)^{n × t}

P is the starting amount, r the yearly rate as a decimal (8% = 0.08), n the number of times interest is added each year, and t the time in years. For continuous compounding, A = P × e^r×t.

How much the frequency changes the result

Going from yearly to daily adds about ₹6,600 here. Going from 8% to 9% adds far more. The rate and the number of years matter most.

Effective yearly rate

Effective rate = (1 + r ÷ n)ⁿ − 1

8% compounded quarterly is (1.02)⁴ − 1 = 8.24% a year. Use this figure to compare a deposit that compounds quarterly with one that compounds monthly or yearly.

Adding money every month

The compound interest calculator also takes a monthly addition. ₹1,00,000 plus ₹2,000 at the end of every month, at 8% compounded quarterly for 10 years, grows to about ₹5,85,621 from ₹3,40,000 put in.

The rule of 72

72 ÷ rate gives the rough years to double. At 8%, about 9 years.

How to use the calculator

1. Enter the starting amount and the yearly rate.
2. Choose the years and how often interest is added.
3. Add a monthly amount if you will keep saving, then compare the compound line with the simple-interest line on the chart.

For a bank deposit, the FD calculator uses the same formula. For loans where interest is not compounded, see the simple interest formula.