How to Calculate Compound Interest

The formula that Einstein allegedly called "the eighth wonder of the world" — and how to use it correctly.

QUICK ANSWER

Formula: A = P(1 + r/n)^(nt) — where P = principal, r = annual rate (as a decimal), n = compounding periods per year, t = years. Example: $5,000 at 4% compounded monthly for 5 years: A = 5,000 × (1 + 0.04/12)^60 = 5,000 × 1.22099 = $6,104.98. Interest earned: $1,104.98.

The Compound Interest Formula Explained

A = P(1 + r/n)nt

  • A = Final amount (principal + interest)
  • P = Principal (your starting amount)
  • r = Annual interest rate as a decimal (6% = 0.06)
  • n = Number of times interest compounds per year
  • t = Time in years

To find only the interest earned: Interest = A − P

1
Write down your variables

P = your starting amount. r = annual rate ÷ 100 (e.g. 6% → 0.06). n = 12 for monthly, 365 for daily, 4 for quarterly, 1 for annually. t = number of years.

2
Calculate r/n

Divide the annual rate by the number of compounding periods. Monthly at 6%: 0.06 ÷ 12 = 0.005 per month.

3
Calculate (1 + r/n)^nt

Add 1 to get the growth factor per period. Raise it to the power of (n × t). Monthly for 5 years = 60 periods. (1.005)^60 = 1.34885.

4
Multiply by P

A = P × (1 + r/n)^nt. If P = $10,000: $10,000 × 1.34885 = $13,488.50. Interest earned = $3,488.50.

Impact of Compounding Frequency

$10,000 at 5% per year for 10 years:

Compounding n (per year) Final Amount Interest Earned
Annually 1 $16,288.95 $6,288.95
Quarterly 4 $16,436.19 $6,436.19
Monthly 12 $16,470.09 $6,470.09
Weekly 52 $16,485.55 $6,485.55
Daily 365 $16,486.65 $6,486.65
Continuously ∞ $16,487.21 $6,487.21

Frequently Asked Questions

What is the difference between simple and compound interest? ▾
Simple interest: you only earn interest on the original principal each period. Compound interest: you earn interest on the principal AND on previously earned interest. On $10,000 at 5% for 10 years — simple = $5,000 interest; compound (annual) = $6,288.95. The difference grows dramatically over longer periods.
How do I calculate compound interest on a savings account? ▾
Use A = P(1 + r/n)^(nt). For a savings account: P = your deposit, r = annual interest rate ÷ 100, n = 12 (most savings accounts compound monthly), t = years. Subtract P from A to find interest earned. Also check whether the rate is APR (nominal) or APY/AER (effective annual rate including compounding).
What is APY vs APR? ▾
APR (Annual Percentage Rate) is the nominal rate before compounding effects. APY (Annual Percentage Yield, US) or AER (Annual Equivalent Rate, UK) is the effective rate AFTER compounding — what you actually earn in a year. A 6% APR compounded monthly is actually 6.168% APY. Always compare APY/AER when shopping for savings accounts.
How does the Rule of 72 work? ▾
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6% annual rate: 72 ÷ 6 = 12 years to double. At 8%: 9 years. At 3%: 24 years. This is a useful mental math shortcut — exact answer would come from solving (1 + r)^t = 2.

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