1. **State the problem:** En. Haikal borrows 20000 at 7.5% annual interest compounded monthly. We want to find: a) Monthly payments for a 7-year loan. b) Savings by choosing a 5-year loan instead of 7 years. 2. **Identify variables:** Principal $P = 20000$ Annual interest rate $r = 7.5\% = 0.075$ Monthly interest rate $i = \frac{0.075}{12} = 0.00625$ Number of months for 7 years $n_7 = 7 \times 12 = 84$ Number of months for 5 years $n_5 = 5 \times 12 = 60$ 3. **Monthly payment formula for amortized loan:** $$ M = P \times \frac{i(1+i)^n}{(1+i)^n - 1} $$ 4. **Calculate monthly payment for 7-year loan:** $$ M_7 = 20000 \times \frac{0.00625(1+0.00625)^{84}}{(1+0.00625)^{84} - 1} $$ Calculate $(1+0.00625)^{84} = (1.00625)^{84} \approx 1.747422$ So, $$ M_7 = 20000 \times \frac{0.00625 \times 1.747422}{1.747422 - 1} = 20000 \times \frac{0.010921}{0.747422} \approx 20000 \times 0.01461 = 292.20 $$ 5. **Calculate monthly payment for 5-year loan:** $$ M_5 = 20000 \times \frac{0.00625(1+0.00625)^{60}}{(1+0.00625)^{60} - 1} $$ Calculate $(1.00625)^{60} \approx 1.42576$ So, $$ M_5 = 20000 \times \frac{0.00625 \times 1.42576}{1.42576 - 1} = 20000 \times \frac{0.008911}{0.42576} \approx 20000 \times 0.02093 = 418.60 $$ 6. **Calculate total payments:** For 7 years: $$ \text{Total}_7 = M_7 \times 84 = 292.20 \times 84 = 24544.80 $$ For 5 years: $$ \text{Total}_5 = M_5 \times 60 = 418.60 \times 60 = 25116.00 $$ 7. **Calculate savings:** Savings by choosing 5-year loan instead of 7-year loan: $$ \text{Savings} = \text{Total}_7 - \text{Total}_5 = 24544.80 - 25116.00 = -571.20 $$ Since this is negative, actually the 5-year loan costs more overall. **Interpretation:** The 5-year loan has higher monthly payments and total cost is higher by 571.20. **Final answers:** a) Monthly payment for 7-year loan is approximately $292.20$ b) He will pay $571.20$ more with the 5-year loan, so no savings but extra cost.