Arithmetic (Beginner) · Quick Reference

Compound Interest Cheat Sheet

Arithmetic (Beginner) · Lesson 16/21

In one line: compound interest is calculated on the principal plus any interest already earned, so the amount grows faster over time than with simple interest.

Key Ideas

1Compounding. Interest is added to the principal at regular intervals, and future interest is calculated on this new, larger amount.

2Compound Interest Formula. Amount = P x (1 + R/100)^T, where T is the number of compounding periods.

3Finding CI. Compound Interest = Amount - Principal.

4Compounding Frequency. Interest can compound annually, semi-annually, quarterly, or monthly; the rate and time must match the compounding period.

5CI vs. SI. Compound interest is always equal to or greater than simple interest for the same P, R, T (for T > 1), because it earns 'interest on interest'.

Worked Examples

Find the compound interest on $1,000 at 10% per year for 2 years.

$210

Find the amount on $2,000 at 5% per year for 3 years, compounded annually.

$2,315.25

Compare SI and CI on $5,000 at 10% for 2 years.

SI = $1,000, CI = $1,050

Formulas

Amount = P x (1 + R/100)^T

CI = Amount - P

Practice Yourself

Find CI on $1,000 at 10% for 1 year.

$100 (same as SI for year 1)

Find the amount on $1,500 at 20% for 2 years, compounded annually.

$2,160

Find CI on $2,000 at 10% for 2 years.

$420