1. **State the problem:** Sam agrees to pay $5,000 per month for 5 years on a car loan at 6.3% annual interest compounded monthly. We need to find the present value (PV) of the car loan. 2. **Formula used:** The present value of an annuity formula is $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ where: - $P$ is the monthly payment, - $r$ is the monthly interest rate (annual rate divided by 12), - $n$ is the total number of payments (months). 3. **Calculate the values:** - Monthly payment $P = 5000$ - Annual interest rate = 6.3%, so monthly interest rate $r = \frac{6.3}{100 \times 12} = 0.00525$ - Number of payments $n = 5 \times 12 = 60$ 4. **Substitute into the formula:** $$PV = 5000 \times \frac{1 - (1 + 0.00525)^{-60}}{0.00525}$$ 5. **Calculate the power term:** $$ (1 + 0.00525)^{-60} = (1.00525)^{-60} $$ 6. **Evaluate:** $$ (1.00525)^{60} \approx 1.372786 $$ So, $$ (1.00525)^{-60} = \frac{1}{1.372786} \approx 0.7281 $$ 7. **Calculate numerator:** $$ 1 - 0.7281 = 0.2719 $$ 8. **Calculate fraction:** $$ \frac{0.2719}{0.00525} \approx 51.84 $$ 9. **Calculate present value:** $$ PV = 5000 \times 51.84 = 259,200 $$ 10. **Final answer:** The present value of the car loan is approximately **259,200**. This means the loan amount Sam is effectively borrowing is about 259,200, which is the amount needed today to cover all future payments at the given interest rate.