1. **State the problem:** Calculate the monthly payment, total payment, and total interest for a loan of 11500 at 5.9% annual interest over 4 years with monthly payments.
2. **Formula for monthly payment:**
$$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$
where $M$ is monthly payment, $P=11500$, $r=\frac{5.9}{100 \times 12} = 0.0049166667$, and $n=4 \times 12 = 48$.
3. **Calculate $(1+r)^n$:**
$$(1 + 0.0049166667)^{48} = 1.270477$$
4. **Calculate numerator and denominator:**
Numerator: $r(1+r)^n = 0.0049166667 \times 1.270477 = 0.006246$
Denominator: $(1+r)^n - 1 = 1.270477 - 1 = 0.270477$
5. **Calculate fraction:**
$$\frac{0.006246}{0.270477} = 0.02309$$
6. **Calculate monthly payment:**
$$M = 11500 \times 0.02309 = 265.54$$
7. **Calculate total payment:**
$$\text{Total payment} = M \times n = 265.54 \times 48 = 12745.92$$
8. **Calculate total interest:**
$$\text{Interest} = \text{Total payment} - P = 12745.92 - 11500 = 1245.92$$
**Final answers:**
(a) Monthly payment = $265.54$
(b) Total payment = $12745.92$
(c) Total interest = $1245.92$
Loan Payment 711A62
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