How to Calculate Compound Interest (With an Example)

Compound interest is interest paid on your interest. You put money in, it earns interest, and then that interest starts earning interest of its own. The formula is A = P(1 + r/n)^(nt): your final amount equals your starting amount times one plus the interest rate, raised to the power of how many times interest is added. It looks forbidding, but once you know what each letter stands for, the arithmetic is just a few multiplications — and the result explains why starting early beats starting big.

By Calcly Team · Last updated 8 November 2026 · Free guide

The compound interest formula, piece by piece

Every symbol in A = P(1 + r/n)^(nt) means something ordinary. P is the principal, the amount you start with. r is the annual interest rate written as a decimal, so 5% becomes 0.05. n is how many times a year interest is added — 1 for yearly, 4 for quarterly, 12 for monthly, 365 for daily. t is the number of years. The part in brackets, (1 + r/n), is what your money is multiplied by at each compounding step; the power, nt, is how many of those steps happen in total. So with yearly compounding, n is 1 and the formula shortens to A = P(1 + r)^t, which is the version most people actually use. A common mistake is to write the rate as 5 instead of 0.05 — if you do that, the answer comes out absurdly large, which is your cue to fix it. Another is to forget that the rate and the time must use the same units: an annual rate needs years, not months.

Worked example: $1,000 at 5% for 10 years

Put $1,000 in an account paying 5% a year, compounded yearly, and leave it for 10 years. The formula gives A = 1,000 × (1 + 0.05)^10 = 1,000 × 1.05^10. Now 1.05^10 is 1.6289, so the final amount is $1,628.89. You earned $628.89 of interest on a $1,000 deposit — more than half your starting amount again, without adding a cent. Compare that with simple interest, which only pays on the original $1,000: 1,000 × 0.05 × 10 = $500, for a total of $1,500. Compounding added $128.89 over the same ten years, and the gap grows with time. Stretch the same example to 20 years and simple interest gives $2,000 while compounding gives 1,000 × 1.05^20 = $2,653.30. At 30 years it is $2,500 against $4,321.94. The longer money sits, the more compounding does the heavy lifting — which is why the same 5% feels boring over one year and remarkable over thirty.

How often interest compounds matters — a little

Take the same $1,000 at 5% for 10 years, but compound it monthly instead of yearly. Now n is 12, so each month your money is multiplied by (1 + 0.05/12) = 1.0041667, and there are 120 monthly steps. The result is about $1,647.01 — roughly $18 more than yearly compounding. Daily compounding would add a few dollars more again. So frequency helps, but it is a small effect next to the two things that actually move the result: the interest rate and the time. Raising the rate from 5% to 6% on that same $1,000 over 10 years takes the total from $1,628.89 to $1,790.85 — a $162 difference, nine times bigger than the monthly-compounding bonus. And adding ten more years at 5% takes it to $2,653.30. If you are choosing between accounts, compare the rate first, the fees second, and the compounding frequency last.

Adding monthly contributions

Most people do not just leave a lump sum sitting — they add a bit each month, and that changes the picture completely. Suppose you start with the same $1,000 at 5%, and add $100 at the end of every month for 10 years. Your starting $1,000 grows to about $1,647, as above. Your contributions are a separate pile: each $100 deposit earns interest for however many months are left, and together they grow to about $15,528. Add the two piles and you end up with roughly $17,175. You paid in $13,000 in total ($1,000 at the start plus $100 × 120 months), so about $4,175 of the final amount is interest — nearly a third of what you have. Notice what did the work here: the monthly habit. Without the contributions, ten years at 5% turns $1,000 into $1,647. With them, the same ten years turns $13,000 of deposits into $17,175. That is the part of compounding most people miss — it rewards the person who keeps adding, not just the person who started with a lot.

The rule of 72

If you want a quick answer without any powers at all, use the rule of 72: divide 72 by your annual interest rate and you get roughly how many years it takes your money to double. At 6%, money doubles in about 12 years. At 8%, about 9 years. At 4%, about 18 years. It is an approximation — the exact answer comes from the formula — but it is close enough to compare options in your head, and it makes the cost of waiting vivid: at 7%, every ten years you delay costs you a doubling. It also works in reverse. If someone promises to double your money in 6 years, they are implying a rate of about 12% a year (72 ÷ 6) — which is the point at which you should start asking very careful questions about risk.

Want the numbers for your own savings? Use our compound interest calculator — enter your starting amount, rate and monthly contribution and it shows the growth year by year. To work out what to save each month for a target, try our savings goal calculator, or our loan calculator to see the same maths working against you on a debt.