Compound Interest Formula: A = P(1 + r/n)^nt Explained
Use the compound interest formula to find account balances, and see why compounding more often earns more, with two worked examples.
The formula
- A = P(1 + r/n)^(nt)
- P = principal, r = rate, n = times per year, t = years
Write r as a decimal: 4% = 0.04.
Example 1
$2,000 earns 4% compounded yearly for 5 years. Find the balance.
- P = 2000, r = 0.04, n = 1, t = 5
- A = 2000(1.04)⁵
- = 2000 × 1.2167
A ≈ $2,433.31
Example 2
What is simple interest on $2,000 at 4% for 5 years, and how much more does compounding earn?
- Simple interest = 2000 × 0.04 × 5 = $400
- Compound interest = 2,433.31 − 2,000 = $433.31
- Difference = 433.31 − 400
Compounding earns about $33.31 more
Common mistake
Using r = 4 instead of 0.04
Convert the percent to a decimal.
n counts compounding periods per year, not total.
Check that your answer is larger than P.
Want more Economics practice?
The free Economics study guide has quizzes, flashcards and practice exams. 100% free, no sign-up needed.
Open the Economics guide