Success Homeschool

Year 10 Mathematics · Compound interest and depreciation

Name: ______________________

Date: ____________

1. Which formula gives the final amount A when a principal P earns compound interest at rate r per period for n periods?
- ☐ (a) A = Prn
- ☐ (b) A = P + rn
- ☐ (c) A = P(1 − r)^n
- ☐ (d) A = P(1 + r)^n
2. $1000 is invested at 10% p.a., compounded annually, for 2 years. What is the final amount?
- ☐ (a) $1200
- ☐ (b) $1210
- ☐ (c) $1100
- ☐ (d) $1221
3. An account pays 8% p.a., compounded quarterly. What is the interest rate per quarter?
- ☐ (a) 8%
- ☐ (b) 4%
- ☐ (c) 0.67%
- ☐ (d) 2%
4. The same principal is invested for 5 years at the same yearly rate. Which earns more interest?
- ☐ (a) Simple interest
- ☐ (b) They are always equal
- ☐ (c) Compound interest
- ☐ (d) It depends only on the principal
5. Interest is compounded monthly for 3 years. How many compounding periods is that?
- ☐ (a) 36
- ☐ (b) 3
- ☐ (c) 12
- ☐ (d) 4
6. $500 is invested at 4% p.a., compounded annually, for 2 years. Find the final amount in dollars.
7. $4000 is invested at 5% p.a., compounded annually, for 2 years. How much interest is earned, in dollars?
8. A laptop costs $1500 and depreciates at 20% p.a. What is its value after 2 years, in dollars?

Answer sheet

1. A = P(1 + r)^n — Each period multiplies the balance by (1 + r), so after n periods A = P(1 + r)^n. The formula with (1 − r) models depreciation.
2. $1210 — A = 1000 × 1.1^2 = 1000 × 1.21 = $1210.
3. 2% — There are 4 quarters in a year, so the rate per quarter is 8% ÷ 4 = 2%.
4. Compound interest — After the first year, compound interest also earns interest on previous interest, so it grows faster than simple interest.
5. 36 — There are 12 months in each year, so n = 3 × 12 = 36.
6. $540.80 — A = 500 × 1.04^2 = 500 × 1.0816 = $540.80.
7. $410 — A = 4000 × 1.05^2 = 4000 × 1.1025 = $4410. Interest = 4410 − 4000 = $410.
8. $960 — A = 1500 × 0.8^2 = 1500 × 0.64 = $960.