Simple interest grows on the original amount only. Compound interest grows on the original amount plus all interest earned so far. Over short periods the difference is small. Over long periods it is enormous. The two formulas show exactly why.
The two formulas
Simple interest: I = P x r x t, where P is principal, r is the annual rate as a decimal, and t is time in years. Total amount A = P x (1 + r x t). Compound interest: A = P x (1 + r/n)^(n x t), where n is compounding periods per year. Compound interest CI = A – P.
With annual compounding, n = 1. With monthly compounding, n = 12 and the rate per period is r/12. More frequent compounding always gives slightly more, because interest starts earning interest sooner.
Worked example: same money, both methods
$10,000 at 5% for 10 years. Simple: I = 10,000 x 0.05 x 10 = $5,000, total $15,000. Compound annually: A = 10,000 x (1.05)^10 = $16,289, interest $6,289. The difference is $1,289 after 10 years. Stretch to 30 years: simple gives $25,000, compound gives $43,219. The gap grows from $1,289 to $18,219, because compounding accelerates while simple interest plods linearly.
Monthly example: $5,000 at 4.5% compounded monthly for 5 years. A = 5,000 x (1 + 0.045/12)^60 = $6,258.98, interest $1,258.98. Compounded annually the same money gives $6,230.92, so monthly compounding adds about $28 over five years. Frequency matters, but rate and time matter far more.
Borrower versus saver
Compound interest helps savers and hurts borrowers. A saver wants compounding as often as possible and as long as possible. A borrower wants simple interest or short terms, because compound interest on a loan means paying interest on interest. This is why short-term loans often use simple interest while mortgages, credit cards, and long investments compound.
Watch for products labelled simple that compound monthly in the fine print. The label matters less than the formula in the terms: check how often interest is added to the balance.
The difference formula
The difference between compound and simple interest on the same money is CI – SI. For the 10-year example: $6,289 – $5,000 = $1,289. For a quick estimate, remember the difference is zero in year one (both give P x r), then grows every year after, roughly with the square of time for small rates. If a deal promises compound growth, ask for the year-by-year table, not just the final number.
The rule of 72
The rule of 72 estimates how long money takes to double under compound interest: years to double is roughly 72 divided by the annual rate. At 6%, money doubles in about 12 years. At 8%, about 9 years. At 12%, about 6 years.
The rule works for compound interest only, and it is an approximation that is most accurate for rates between 6% and 10%. For simple interest there is no doubling shortcut of the same kind, because simple growth is linear: doubling always takes 100 / rate years. At 6% simple, doubling takes about 16.7 years, versus 12 under compounding.
Try it faster with the tool
You can follow every step above by hand, but the free Simple Interest and Compound Interest Calculator does the arithmetic for you. Enter your numbers and it gives the answer right away, so you can check your hand calculation or skip straight to the result.
Quick tips
- Simple: interest on principal only. Compound: interest on principal plus past interest.
- Difference is zero in year one, then grows every year.
- Check compounding frequency in the fine print.