Lesson 1 of 4 · Form 3 Mathematics
Compound interest and depreciation
18 min
Simple interest
I = PRT ÷ 100, where P is principal, R is rate per year (%), T is time in years.
Compound interest
Interest is added to the principal each period.
- A = P(1 + r/100)ⁿ
- Compound interest = A - P
Example: KES 10,000 at 10% p.a. for 2 years:
A = 10,000 × 1.1² = 12,100. Interest = 2,100.
Compounded more often
Half-yearly: use r/2 and 2n periods. Quarterly: r/4 and 4n.
Depreciation
Value falls by a fixed % each year:
- A = P(1 - r/100)ⁿ
Example: A car worth 800,000 depreciates at 20% p.a. After 2 years: 800,000 × 0.8² = 512,000.
Hire purchase
Total cost = deposit + (instalment × number of instalments). Extra paid = total - cash price.
Key points to remember
- A = P(1 + r/100)ⁿ
- Interest = A - P
- Depreciation: A = P(1 - r/100)ⁿ
- Half-yearly: halve the rate, double the periods
Test yourself
