How Compound Interest Works, with Worked Examples You Can Recalculate

Simple interest vs compound interest

Simple interest pays (or charges) interest only on the original principal. Compound interest pays interest on principal plus accumulated interest. That small wording difference is why long-term savings curves bend upward and why unpaid credit balances become painful.

Basic compound formula for annual compounding:

A = P (1 + r)^t

• A = amount after t years
• P = starting principal
• r = annual interest rate in decimal form
• t = time in years

Worked example 1: savings with annual compounding

You invest $5,000 at 6% compounded annually for 10 years.

A = 5000 × (1.06)¹⁰

(1.06)¹⁰ ≈ 1.7908

A ≈ $8,954

Interest earned ≈ $3,954. With simple interest at 6% for 10 years, interest would be only 5000 × 0.06 × 10 = $3,000, for a total of $8,000. Compounding added about $954 beyond simple interest in this scenario.

Worked example 2: more frequent compounding

Same $5,000 at 6% for 10 years, compounded monthly:

A = P (1 + r/n)^nt

n = 12, r = 0.06, t = 10

A = 5000 × (1 + 0.06/12)¹²⁰ = 5000 × (1.005)¹²⁰ ≈ 5000 × 1.8194 ≈ $9,097

Monthly compounding earns a bit more than annual compounding at the same nominal rate because interest starts earning interest sooner.

Worked example 3: regular monthly contributions

Many people do not deposit once. Suppose you start at $0 and contribute $200 per month for 10 years at 6% annual return compounded monthly. Future value of an ordinary annuity (deposit at period end) is approximately:

FV = PMT × [((1 + i)ⁿ − 1) / i]

where i = 0.06/12 = 0.005, n = 120, PMT = 200

((1.005)¹²⁰ − 1) / 0.005 ≈ (1.8194 − 1) / 0.005 ≈ 163.88

FV ≈ 200 × 163.88 ≈ $32,776

Total contributions = $24,000. Implied growth ≈ $8,776. The exact result depends on deposit timing and real returns; the lesson is that steady contributions plus compounding dominate “waiting for a better time.”

Worked example 4: compounding working against you

A $2,000 credit balance at 22% APR compounded monthly, if you pay only tiny amounts, grows quickly. Monthly rate ≈ 0.22/12 ≈ 0.01833. After 12 months with no payments (illustrative extreme), balance ≈ 2000 × (1.01833)¹² ≈ $2,489. Real statements include fees and payment rules, but the direction is clear: high-rate compounding favors the lender.

Rule of 72 for mental estimates

Divide 72 by the annual rate to estimate doubling time. At 6%, 72 / 6 = 12 years approximate doubling. At 9%, about 8 years. It is an estimate, not a contract, but it helps compare options without a spreadsheet.

How to use online calculators well

1. Match compounding frequency to what the account or loan actually uses.
2. Separate nominal APR from APY when banks advertise both.
3. For loans, look at amortization: early payments are mostly interest.
4. Run optimistic and pessimistic rates for long horizons.

Compound interest is repeated multiplication. Start earlier, contribute consistently, and avoid high-rate debt when you can. Recalculate examples with a compound interest or loan calculator until the curve feels intuitive—then your long-term decisions get easier.