Simple vs Compound Interest: How Money Really Grows

Simple interest is paid only on the money you started with. Compound interest is paid on the starting amount plus the interest already earned, so the growth speeds up over time. The difference is small in year one and large after a decade.

The formulas

Simple:      A = P(1 + rt)
Compound:    A = P(1 + r/n)ⁿᵗ
Continuous:  A = Peʳᵗ

P is the starting amount, r the yearly rate as a decimal, t the number of years, and n how many times a year interest is added.

10,000 at 6% for 10 years

Compounding monthly earns about 2,194 more than simple interest over the same 10 years, with the same rate and the same starting amount.

Does compounding frequency matter?

Yes, but less than you might expect. Going from yearly to monthly compounding adds about 285 here; going from monthly to continuous adds only 27. The rate and the number of years matter far more than the frequency.

Banks often quote an effective annual rate to make offers comparable. A 6% rate compounded monthly is equivalent to about 6.17% compounded once a year.

The rule of 72

To estimate how long money takes to double, divide 72 by the yearly rate. At 6%, money doubles in about 72 ÷ 6 = 12 years. The exact answer is 11.9 years, so the shortcut is very close for typical rates.

The same math works against you

Loans and credit cards also compound. An unpaid balance grows the same way savings do, which is why paying debt early saves more than the headline rate suggests.

Tip These examples are for learning. For real financial decisions, check the exact terms of the account or loan.

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Frequently asked questions