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Finance & Business · pattern A, Numeric fields

Compound interest, with the compounding frequency exposed.

Enter a principal, rate, term and compounding frequency for the maturity value, the interest earned and the effective annual rate the nominal figure hides.

Inputs

The formula used

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

P is the principal, r the nominal annual rate, n the compounding periods per year and t the years. Monthly compounding uses n = 12.

Balance at maturity

2,697.70

Interest earned
697.70
Growth factor
1.348850
Effective annual rate
6.1678 %
If compounded annually instead
2,676.45
Simple interest for comparison
2,600.00
Years to double at this rate
11.581

Nominal and effective rates are different numbers.

A 6% nominal rate compounded monthly is an effective 6.168% a year, because interest earns interest within the year. Advertised rates are usually nominal and comparison figures such as APR or AER are effective, which is why two products quoting the same headline rate can pay differently. Always compare effective rates.

Questions about compound interest

What is the rule of 72?
Dividing 72 by the percentage rate approximates the doubling time. At 6% it gives twelve years against an exact 11.58 — close enough for mental arithmetic.
Does more frequent compounding always help?
Yes, but with diminishing returns. Moving from annual to monthly matters; monthly to daily adds a few hundredths of a per cent.
What is continuous compounding?
The limit as frequency goes to infinity, giving A = Pe^(rt). It is the standard model in derivative pricing and an upper bound on discrete compounding.

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