1. **State the problem:** You take a loan of 120000 with an annual interest rate of 4.7% compounded monthly for 20 years. (a) Find the monthly loan payment. (b) Find the total interest paid. 2. **Identify the formula for monthly payment:** The formula for monthly payment $M$ on a loan principal $P$ with monthly interest rate $r$ over $n$ months is: $$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$$ 3. **Calculate monthly interest rate $r$ and number of payments $n$:** Annual interest rate = 4.7%, so monthly interest rate: $$r = \frac{4.7}{100} \times \frac{1}{12} = 0.0039167$$ Number of months in 20 years: $$n = 20 \times 12 = 240$$ 4. **Calculate monthly payment $M$:** Plug in values: $$M = 120000 \times \frac{0.0039167 (1 + 0.0039167)^{240}}{(1 + 0.0039167)^{240} - 1}$$ Calculate $(1+r)^n$: $$ (1 + 0.0039167)^{240} \approx 2.5820 $$ Then: $$M = 120000 \times \frac{0.0039167 \times 2.5820}{2.5820 - 1} = 120000 \times \frac{0.010108}{1.5820} = 120000 \times 0.006389 = 766.68$$ So monthly payment is approximately **766.68**. 5. **Calculate total interest paid:** Total payment over 240 months: $$240 \times 766.68 = 184003.20$$ Total interest paid: $$184003.20 - 120000 = 64003.20$$ **Final answers:** - (a) Monthly payment = $766.68$ - (b) Total interest paid = $64003.20$