How to Calculate Compound Interest by Hand, Step by Step

Compound interest grows faster than simple interest because each period's interest gets added to the balance before the next period's interest is calculated -- you earn interest on your interest. Here's exactly how to work it out by hand.

The Formula

A = P × (1 + r/n)^n×t

Where A is the final amount, P is the principal (starting amount), r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years.

Worked Example

1. 1

   Set up your numbers

   $1,000 principal, 6% annual rate (r = 0.06), compounded monthly (n = 12), for 3 years (t = 3).

2. 2

   Divide the rate by the compounding frequency

   0.06 ÷ 12 = 0.005 per month.

3. 3

   Add 1, then raise to the power of (n × t)

   (1 + 0.005)^12×3 = 1.005³⁶ ≈ 1.1967.

4. 4

   Multiply by the principal

   $1,000 × 1.1967 ≈ $1,196.70 -- $196.70 in total interest over 3 years.

Simple Interest, for Comparison

Simple interest on the same loan would just be $1,000 × 0.06 × 3 = $180 total -- compounding monthly earned about $16.70 more over the same 3 years purely from interest-on-interest.

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Frequently Asked Questions

Does more frequent compounding always mean meaningfully more growth?

The gains shrink as compounding gets more frequent -- daily compounding only slightly beats monthly, which only slightly beats quarterly, because you're approaching the mathematical limit called continuous compounding. The biggest jump is going from annual to monthly, not from monthly to daily.

Can this formula be used for compounding debt, like credit cards?

Yes -- the same formula models compounding debt growth, which is exactly why credit card balances can snowball if only the minimum payment is made: unpaid interest gets added to the balance and starts earning its own interest the very next period.