Question: Sharette took out a $1,280, 6-year loan with an APR of 8.15% to buy a new computer. a. What is the monthly payment? The monthly payment is $ $. b. At the end of the 6-year term, how much money will she have paid for the computer? She will have paid $ $. c. What is the interest charge? The interest charge is $ $.

1. **State the problem:** Sharette took out a loan of $1280$ dollars for $6$ years with an APR of $8.15\%$. We need to find: a. The monthly payment. b. The total amount paid after 6 years. c. The interest charged. 2. **Formula for monthly payment on an installment loan:** $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where: - $M$ is the monthly payment, - $P$ is the principal amount ($1280$), - $r$ is the monthly interest rate (APR divided by 12), - $n$ is the total number of payments (months). 3. **Calculate monthly interest rate $r$ and total payments $n$: ** $$r = \frac{8.15}{100 \times 12} = \frac{8.15}{1200} = 0.0067917$$ $$n = 6 \times 12 = 72$$ 4. **Calculate $(1+r)^n$: ** $$ (1 + 0.0067917)^{72} = 1.0067917^{72} \approx 1.60103$$ 5. **Calculate numerator and denominator for the formula:** Numerator: $$r(1+r)^n = 0.0067917 \times 1.60103 = 0.01087$$ Denominator: $$(1+r)^n - 1 = 1.60103 - 1 = 0.60103$$ 6. **Calculate monthly payment $M$: ** $$M = 1280 \times \frac{0.01087}{0.60103} = 1280 \times 0.01809 = 23.16$$ 7. **Calculate total amount paid over 6 years: ** $$\text{Total paid} = M \times n = 23.16 \times 72 = 1667.52$$ 8. **Calculate interest charged: ** $$\text{Interest} = \text{Total paid} - \text{Principal} = 1667.52 - 1280 = 387.52$$ **Final answers:** - a. Monthly payment is $\boxed{23.16}$. - b. Total amount paid is $\boxed{1667.52}$. - c. Interest charged is $\boxed{387.52}$.