How to Calculate Compound Interest
Compound interest is interest earned on interest: each period's growth is added to the balance, and the next period's interest is calculated on that larger balance. Over long periods this snowball effect dwarfs the original contributions.
The compound interest formula
The future value of a one-time investment is:
A = P (1 + r/n)^(n t)- A \u2014 final amount (principal + interest)
- P \u2014 principal (the amount you invest)
- r \u2014 annual interest rate as a decimal (12% = 0.12)
- n \u2014 compounding periods per year (12 for monthly, 4 for quarterly, 1 for yearly)
- t \u2014 time in years
The compound interest earned is simply A \u2212 P.
Step-by-step example
Invest \u20B91,00,000 at 10% p.a., compounded yearly, for 10 years:
- Convert the rate: r = 10% = 0.10, and with yearly compounding n = 1.
- Growth factor per year: 1 + 0.10/1 = 1.10.
- Number of periods: n \u00D7 t = 1 \u00D7 10 = 10.
- Future value: A = 1,00,000 \u00D7 1.10^10 = 1,00,000 \u00D7 2.59374 = \u20B92,59,374.
- Interest earned: 2,59,374 \u2212 1,00,000 = \u20B91,59,374.
Notice the interest earned exceeds the principal \u2014 that is compounding at work. Year by year it looks like this:
| Year | Opening Balance | Interest @10% | Closing Balance |
|---|---|---|---|
| 1 | \u20B91,00,000 | \u20B910,000 | \u20B91,10,000 |
| 2 | \u20B91,10,000 | \u20B911,000 | \u20B91,21,000 |
| 3 | \u20B91,21,000 | \u20B912,100 | \u20B91,33,100 |
| 5 | \u20B91,46,410 | \u20B914,641 | \u20B91,61,051 |
| 10 | \u20B92,35,795 | \u20B923,579 | \u20B92,59,374 |
Compounding frequency
The same nominal rate credited more often produces a higher effective return, because interest starts earning interest sooner. For \u20B91,00,000 at 10% over 10 years:
| Compounding | n | Future Value | Effective Annual Rate |
|---|---|---|---|
| Yearly | 1 | \u20B92,59,374 | 10.00% |
| Half-yearly | 2 | \u20B92,65,330 | 10.25% |
| Quarterly | 4 | \u20B92,68,506 | 10.38% |
| Monthly | 12 | \u20B92,70,704 | 10.47% |
Monthly investments (SIP)
When you invest a fixed amount every month, each instalment compounds for a different length of time. The closed-form future value is:
FV = M \u00D7 [ ((1 + i)^m \u2212 1) / i ] \u00D7 (1 + i)where M is the monthly instalment, i the monthly rate (annual rate \u00F7 12) and m the number of months. In practice it is easier to let the SIP Calculator simulate it month by month \u2014 which also lets you adjust for inflation.
The Rule of 72
A quick mental shortcut: divide 72 by the annual return to estimate the doubling time. At 8% money doubles in about 9 years; at 12%, about 6 years. Over a 30-year horizon at 12% that is roughly five doublings \u2014 a 32\u00D7 multiple.
Don't forget inflation
A crore twenty years from now will not buy what a crore buys today. Divide the nominal future value by (1 + inflation)^t to get the real value. All calculators on this site show inflation-adjusted results, and the Timeline Simulator plots the real curve alongside the nominal one so the gap is impossible to miss.
Try it yourself
Put the formula to work in the Timeline Simulator, the SIP Calculator or the Lump Sum Calculator \u2014 or first see how much compounding beats simple interest.