In terms of paying less in interest, which is more economical for a \( \$ 130,000 \) mortgage: a 30 -year fixed-rate at \( 9.5 \% \) or a 15 -year fixed-rate at \( 9 \% \) ? How much is saved in interest? Use the following formula to determine the regular payment amount. \[ P M T=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} \] Select the correct choice below and fill in the answer box within your choice. (Do not round until the final answer. Then round to the nearest thousand dollars.) A. The 15 -year \( 9 \% \) loan is more economical. The buyer will save approximately \( \$ \) \( \square \) in interest. B. The 30 -year \( 9.5 \% \) loth is more economical. The buyer will save approximately \( \$ \) \( \square \) in interest.

To calculate the monthly payments for each mortgage using the given formula, we need to define: - \( P \) = principal = \( 130,000 \) - \( r \) = annual interest rate - \( n \) = number of payments per year (12 for monthly) - \( t \) = loan term in years **For the 30-year mortgage at 9.5%:** - \( r = 0.095 \) - \( n = 12 \) - \( t = 30 \) \[ PMT_{30} = \frac{130,000\left(\frac{0.095}{12}\right)}{1-\left(1+\frac{0.095}{12}\right)^{-12 \times 30}} \] Calculating this gives: \[ PMT_{30} \approx 1,147.06 \] The total payment over 30 years: \[ Total_{30} = PMT_{30} \times 12 \times 30 = 1,147.06 \times 360 \approx 413,541.60 \] Interest paid for 30 years: \[ Interest_{30} = Total_{30} - Principal = 413,541.60 - 130,000 \approx 283,541.60 \] **For the 15-year mortgage at 9%:** - \( r = 0.09 \) - \( n = 12 \) - \( t = 15 \) \[ PMT_{15} = \frac{130,000\left(\frac{0.09}{12}\right)}{1-\left(1+\frac{0.09}{12}\right)^{-12 \times 15}} \] Calculating this gives: \[ PMT_{15} \approx 1,084.79 \] The total payment over 15 years: \[ Total_{15} = PMT_{15} \times 12 \times 15 = 1,084.79 \times 180 \approx 195,270.20 \] Interest paid for 15 years: \[ Interest_{15} = Total_{15} - Principal = 195,270.20 - 130,000 \approx 65,270.20 \] **Now we calculate the savings in interest:** \[ Savings = Interest_{30} - Interest_{15} \approx 283,541.60 - 65,270.20 \approx 218,271.40 \] So the answer is: A. The 15-year \( 9 \% \) loan is more economical. The buyer will save approximately \( \$ \) 218,000 in interest.