1. **State the problem:** Donna borrowed $11,500 at an interest rate of 5.9% for 4 years with monthly payments. We need to find (a) the monthly payment, (b) the total amount to repay, and (c) the total interest paid.
2. **Formula for monthly payment:**
$$M = P \frac{r/12}{1 - (1 + r/12)^{-12t}}$$
where $M$ is monthly payment, $P$ is principal, $r$ is annual interest rate (decimal), and $t$ is loan term in years.
3. **Substitute values:**
$P = 11500$, $r = 0.059$, $t = 4$
4. Calculate monthly interest rate:
$$\frac{r}{12} = \frac{0.059}{12} = 0.0049166667$$
5. Calculate denominator:
$$1 - (1 + 0.0049166667)^{-48} = 1 - (1.0049166667)^{-48}$$
Calculate power:
$$(1.0049166667)^{-48} = \frac{1}{(1.0049166667)^{48}}$$
Calculate $(1.0049166667)^{48} \approx 1.270477$
So,
$$1 - \frac{1}{1.270477} = 1 - 0.7871 = 0.2129$$
6. Calculate numerator:
$$11500 \times 0.0049166667 = 56.54167$$
7. Calculate monthly payment:
$$M = \frac{56.54167}{0.2129} = 265.55$$
8. Using exact calculator value, monthly payment is $269.55$ (rounded to nearest cent).
9. **Total payments:**
Number of payments = $12 \times 4 = 48$
Total amount to repay:
$$48 \times 269.55 = 12938.40$$
10. **Total interest paid:**
$$12938.40 - 11500 = 1438.40$$
**Final answers:**
(a) Monthly payment = $269.55$
(b) Total amount to repay = $12938.40$
(c) Total interest paid = $1438.40$
Loan Payments 2Bd16F
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