Calculators/Mathematics/Compound interest

Compound interest

Compounding interest · savings and loans · growth chart

Compound interest — illustration
Compounding
Final capital
16,288.95
Interest
6,288.95
Effective annual rate
5%
Capital growth (10 years)

Formula: Kₙ = K₀·(1 + p/100/m)m·n. For comparison, simple interest would give 15,000.00 — the difference is the effect of "interest on interest".

Compound interest is interest charged also on interest already added — "interest on interest". The balance after nn periods:

Kn=K0(1+p100 m)m nK_n=K_0\left(1+\frac{p}{100\,m}\right)^{m\,n}

where K0K_0 is the initial principal, pp — the annual interest rate, mm — the number of compounding periods per year (annual m=1m=1, quarterly m=4m=4, monthly m=12m=12), and nn — the number of years.

The calculator shows the final balance, total interest, the effective annual rate and a growth chart — and compares the result with simple interest, so you can see the power of compounding.

Examples

$10,000, 5% per year, 10 years (annual compounding)
→ K₁₀ ≈ $16,289 (interest ≈ $6,289)
Same inputs, but monthly compounding
→ K₁₀ ≈ $16,470 — effective rate ≈ 5.12%

Frequently asked questions

How does compound interest differ from simple interest?+

With simple interest you earn interest only on the initial principal. With compound interest the added interest also earns interest, so the balance grows exponentially — the longer the time, the bigger the difference.

What is the effective annual rate?+

It is the real annual growth of the balance once more frequent compounding is taken into account. With monthly compounding, a nominal 5% gives about 5.12% effectively.

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