Compound interest · Grade 11

In Grade 11 you learn: growth and decay formulas.

Compound interest is worked out on the amount in the account each year, including the interest already added, so it grows faster than simple interest. Multiply by the same multiplier every year: A = P(1 + r)ⁿ. Values that fall by a percentage each year (depreciation) work the same way with (1 − r).

Key facts

  • Depreciation (value falls by r each year): A = P(1 − r)ⁿ.
  • Compounded monthly: use the monthly rate (r ÷ 12) and the number of months (12n).

Worked examples

Example 1

A car bought for $18,000 loses 15% of its value each year. What is it worth after 3 years?

Answer: $11,054.25

Example 2

$10,000 is invested at 9% per year, compounded monthly, for 2 years. Find the final amount.

Answer: $11,964.14

Example 3

$6,000 is invested at 2.5% compound interest per year for 4 years. Find its value, to 2 decimal places.

Answer: $6,622.88

Example 4

How many whole years does it take $4,000 to grow to more than $5,000 at 3.5% compound interest?

Answer: 7 years

Other years