1. **State the problem:** Donna borrowed $11500$ at an annual interest rate of $5.9\%$ for $4$ years with monthly payments. We need to find: (a) Monthly payment (b) Total payment over the loan term (c) Total interest paid 2. **Formula for monthly payment of an amortized loan:** $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where: - $M$ = monthly payment - $P = 11500$ (principal) - $r = \frac{5.9}{100 \times 12} = 0.0049166667$ (monthly interest rate) - $n = 4 \times 12 = 48$ (total number of payments) 3. **Calculate monthly payment:** Calculate $r(1+r)^n$: $$r(1+r)^n = 0.0049166667 \times (1 + 0.0049166667)^{48}$$ Calculate $(1+r)^n - 1$: $$ (1 + 0.0049166667)^{48} - 1$$ 4. **Evaluate powers:** $$ (1 + 0.0049166667)^{48} = 1.270477$$ 5. **Substitute values:** $$M = 11500 \times \frac{0.0049166667 \times 1.270477}{1.270477 - 1} = 11500 \times \frac{0.006246}{0.270477}$$ 6. **Simplify fraction:** $$\frac{0.006246}{0.270477} = 0.02309$$ 7. **Calculate monthly payment:** $$M = 11500 \times 0.02309 = 265.54$$ 8. **Total payment over loan term:** $$\text{Total payment} = M \times n = 265.54 \times 48 = 12745.92$$ 9. **Total interest paid:** $$\text{Interest} = \text{Total payment} - P = 12745.92 - 11500 = 1245.92$$ **Final answers:** (a) Monthly payment = $265.54$ (b) Total payment = $12745.92$ (c) Total interest = $1245.92$