Compound Interest
What is Compound Interest?
Compound interest is interest earned on both the original principal and on previously accumulated interest.
Because interest is added back to the balance, savings grow faster over time than with simple interest. The longer the time horizon and the higher the rate, the larger the compounding effect.
Compound Interest: a worked example
Maya deposits $2,500 at 6% compounded annually and leaves it alone for three years. Year one: $2,500 × 1.06 = $2,650. Year two: $2,650 × 1.06 = $2,809. Year three: $2,809 × 1.06 = $2,977.54. Total interest is $477.54, while simple interest would pay only $2,500 × 0.06 × 3 = $450. The $27.54 gap is interest earning interest: 6% of the first year's $150 adds $9 in year two, and 6% of the $309 of accumulated interest adds $18.54 in year three. Stretch the same account to thirty years and it holds about $14,359 against simple interest's $7,000.
The mistake students make with compound interest
The usual slip is plugging an annual rate into a formula that counts months. At 12% compounded monthly for two years, the rate per period is 0.12 ÷ 12 = 0.01 and n is 24, so $1,000 grows to $1,269.73, not $1,000 × 1.12²⁴. Whatever unit n counts, r must match it. A second habit worth breaking: calling three years at 6% a total return of 18%, which ignores compounding and understates the true 19.1%.
Compound Interest questions
What is the difference between simple and compound interest?
Simple interest pays only on the original principal, while compound interest pays on the principal plus every dollar of interest already credited. Put $3,000 at 5% for four years: simple interest gives $600, but annual compounding gives $3,000 × 1.05⁴ = $3,646.52, so $646.52 of interest. The $46.52 gap widens every year, because the balance the rate applies to keeps growing.
How do you calculate compound interest?
Compound interest is calculated by multiplying the principal by (1 + r) once for every compounding period, then subtracting the principal back out. As a formula, FV = P(1 + r)ⁿ. For $500 at 4% a year for three years, FV = $500 × 1.04³ = $562.43, so the interest is $62.43. If the account compounds monthly, r becomes the annual rate divided by twelve and n becomes the number of months.
Does compounding more often earn you more money?
Compounding more often earns more at the same stated annual rate, because each credit of interest starts earning sooner. Take $600 at 12% for one year. Compounded once, the balance is $672. Compounded monthly at 1% per month, it is $600 × 1.01¹² = $676.10, about $4 more. The advantage grows with the rate and the horizon, but it flattens out as compounding approaches continuous.
Formula / Example
Related terms
Common comparisons
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated