Compound interest calculator
Growth of a lump sum at compound interest with yearly, half-yearly, quarterly or monthly compounding, the year-by-year table, and the difference from simple interest.
Enter the amount, the rate and the years.
The formula
Compound interest adds each period's interest to the principal, so the next period's interest is earned on a larger sum. For a principal P at a yearly rate r (as a fraction), compounded n times a year for t years:
A = P × (1 + r ÷ n)^(n × t) compound interest = A − P simple interest = P × r × t
Simple interest never adds the interest back, so it grows in a straight line; compound interest curves upward, slowly at first and steeply later. The gap between them is the interest earned on interest, and it is what makes the number of years matter more than the rate.
Worked example
Rs 1,00,000 at 8% for 10 years. With yearly compounding the amount is Rs 2,15,892; quarterly, Rs 2,20,804; monthly, Rs 2,21,964. Simple interest over the same ten years would give Rs 1,80,000. The compounding frequency adds about Rs 6,000 between yearly and monthly; the ten years add Rs 1,20,000 to Rs 1,22,000 over the principal. Double the time to 20 years at the same quarterly compounding and the amount is Rs 4,87,544: the second decade earns more than twice what the first did.
Where compounding shows up
- Bank fixed deposits compound quarterly; the FD calculator is this formula with n = 4 and tenure in months.
- The Public Provident Fund compounds yearly on the lowest balance between the 5th and the end of each month, at a rate the government sets each quarter.
- Loan interest compounds against you the same way; an EMI is designed to pay each month's interest in full so the balance never compounds, which is why paying less than the EMI is so expensive.
- Credit cards charge monthly on the outstanding amount, so a card's "3% a month" is about 42.6% a year compounded, not 36%.
- Inflation compounds too. At 6% a year, prices double in about 12 years; a sum that grows at 6% only keeps its buying power.
The rule of 72
Dividing 72 by the yearly rate gives the years to double: at 8% about 9 years, at 12% about 6, at 6% about 12. It is an approximation for yearly compounding that is good enough for a conversation, and the calculator gives the exact figure if you type the rate and try years until the amount doubles.