1. **State the problem:** Michael wants to invest 22000 for one year. (a) Calculate amount after one year at 8.58% simple interest. (b) Calculate amount after one year if invested for two 6-month terms at 8.53% each, compounded semi-annually. (c) Find the equivalent one-year interest rate that yields the same amount as in (b). 2. **Part (a): One-year investment at 8.58%** - Interest rate: 8.58% = 0.0858 - Amount after one year: $$A = P(1 + r) = 22000(1 + 0.0858)$$ - Calculate: $$A = 22000 \times 1.0858 = 23887.60$$ 3. **Part (b): Two 6-month terms at 8.53% each, compounded semi-annually** - Semi-annual rate: 8.53% annual means 4.265% per 6 months = 0.04265 - Compound twice: $$A = P(1 + r)^n = 22000(1 + 0.04265)^2$$ - Calculate: $$A = 22000 \times (1.04265)^2 = 22000 \times 1.086163 = 23895.59$$ 4. **Part (c): Equivalent one-year rate to match amount in (b)** - Let equivalent rate be $R$ - Equation: $$22000(1 + R) = 23895.59$$ - Solve for $R$: $$1 + R = \frac{23895.59}{22000} = 1.086163$$ - $$R = 1.086163 - 1 = 0.086163 = 8.62\%$$ **Final answers:** (a) 23887.60 (b) 23895.59 (c) 8.62%