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
- Compound interest: A = P(1 + r)ⁿ.
- 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).
- The multiplier for a 4% rise is 1.04; for a 15% fall it is 0.85.
- Inflation raises prices like compound interest.
Worked examples
Example 1
R20,000 is invested at 5% compound interest per year. Find its value after 2 years.
Answer: R22,050
Example 2
R2,000 is invested at 3% compound interest per year. Find its value after 5 years.
Answer: R2,318.55
Example 3
A house is worth R1,500,000. Its value rises by 4% each year. What is it worth after 3 years?
Answer: R1,687,296
Example 4
R10,000 is invested for 3 years at 5% per year. How much more is it worth with compound interest than with simple interest?
Answer: R76.25
Example 5
A car bought for R18,000 loses 15% of its value each year. What is it worth after 3 years?
Answer: R11,054.25
Example 6
R10,000 is invested at 9% per year, compounded monthly, for 2 years. Find the final amount.
Answer: R11,964.14
Example 7
R60,000 is invested at 2.5% compound interest per year for 4 years. Find its value, to 2 decimal places.
Answer: R66,228.77
Example 8
How many whole years does it take R40,000 to grow to more than R50,000 at 3.5% compound interest?
Answer: 7 years