Compound interest and depreciation

Compound interest as repeated percentage increase, the formula A = P(1 + r)^n, depreciation with A = P(1 − r)^n, and comparing simple and compound interest.

Compound interest

With compound interest, each year's interest is added to the balance, so next year you earn interest on the interest.

$$A = P(1 + r)^n \qquad A = P(1 - r)^n$$

Compound vs simple

1000 dollars invested. The solid compound curve pulls away from the dashed simple line over time.

Example 1●

$\$1000$ is invested at $5\%$ p.a. compounded annually for $2$ years. Find the amount and the interest.

$A = 1000 \times 1.05^2 = \$1102.50$

Interest $= \$102.50$

Example 2●●

A $\$30\,000$ car depreciates by $15\%$ p.a. Find its value after $2$ years.

$A = 30\,000 \times 0.85^2 = 30\,000 \times 0.7225$

$= \$21\,675$

Flashcards

Compound interest

$A = P(1 + r)^n$

Depreciation

$A = P(1 - r)^n$

Interest earned

$A - P$

Practice

$\$1000$ at $5\%$ p.a. compounded annually for $2$ years. Amount?
A $\$30\,000$ car depreciates $15\%$ p.a. Value after $2$ years?
$\$5000$ at $6\%$ p.a. compounded annually for $3$ years. Amount to the nearest cent?
An $\$8000$ machine depreciates $20\%$ p.a. Value after $3$ years?
Interest earned on $\$2000$ at $3\%$ p.a. compounded annually for $4$ years?
$\$1000$ for $10$ years at $8\%$ p.a. Which earns more?
What multiplier is used each year for $4\%$ p.a. compound growth?
What multiplier is used each year for $10\%$ p.a. depreciation?