Subjects finance

Loan Payment 711A62

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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 = $1245.92$