7.5 Simple and Compound Interest

Notes

Interest is the price of using money. The principal is the amount borrowed or saved.

• Simple interest is paid only on the principal: $I = Prt$, where $P$ is principal, $r$ is the yearly rate as a decimal and $t$ is time in years.
• Compound interest is paid on the principal and on interest already earned: $A = P(1 + r)^t$ when interest compounds once a year.
• Worked example (simple): $1,000 at $5\%$ for 3 years earns $1{,}000 \times 0.05 \times 3 = 150$ dollars, for a total of $1,150.
• Worked example (compound): $1{,}000(1.05)^3 = 1{,}000 \times 1.157625 \approx 1{,}157.63$ dollars. Compounding earned $7.63 more.
• Over long periods, compounding makes a large difference. Interest that compounds more often (monthly instead of yearly) grows slightly faster.
• For borrowers, compound interest makes debt grow if it is not paid down.