Questions: Use PMT =(n)/[1-(1+(r/n))^(-n t)] to determine the regular payment amount, rounded to the nearest dollar. In terms of paying less in interest, which is more economical for a 240,000 mortgage: a 30 -year fixed-rate at 9.5% or a 20 -year fixed-rate at 9%? How much is saved in interest? 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 20 -year 9% loan is more economical. The buyer will save approximately in interest. B. The 30 -year 9.5% loan is more economical. The buyer will save approximately in interest.

Use PMT =(n)/[1-(1+(r/n))^(-n t)] to determine the regular payment amount, rounded to the nearest dollar. In terms of paying less in interest, which is more economical for a 240,000 mortgage: a 30 -year fixed-rate at 9.5% or a 20 -year fixed-rate at 9%? How much is saved in interest?

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 20 -year 9% loan is more economical. The buyer will save approximately in interest.
B. The 30 -year 9.5% loan is more economical. The buyer will save approximately in interest.

Transcript text: Use PMT $=\frac{(n)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to determine the regular payment amount, rounded to the nearest dollar. In terms of paying less in interest, which is more economical for a \$240,000 mortgage: a 30 -year fixed-rate at $9.5 \%$ or a 20 -year fixed-rate at $9 \%$ ? How much is saved in interest? 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 20 -year $9 \%$ loan is more economical. The buyer will save approximately \$ $\square$ in interest. B. The 30 -year $9.5 \%$ loan is more economical. The buyer will save approximately \$ $\square$ in interest.

Solution

Solution Steps

Step 1: Calculate the Monthly Payment for Each Loan Option

Using the formula $PMT = \frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-nt}\right]}$, for Loan 1: $PMT_1 = \frac{240000\left(\frac{0.095}{12}\right)}{\left[1-\left(1+\frac{0.095}{12}\right)^{-360}\right]} = 2018.05$ for Loan 2: $PMT_2 = \frac{240000\left(\frac{0.09}{12}\right)}{\left[1-\left(1+\frac{0.09}{12}\right)^{-240}\right]} = 2159.34$

Step 2: Calculate the Total Payments Over the Life of Each Loan

For Loan 1: Total Payments = PMT_1 * n * t1 = 726498.04 For Loan 2: Total Payments = PMT_2 * n * t2 = 518242.15

Step 3: Calculate the Total Interest Paid for Each Loan

For Loan 1: Total Interest = Total Payments - P = 486498.04 For Loan 2: Total Interest = Total Payments - P = 278242.15

Step 4: Compare the Total Interest Paid for Each Loan

Loan 2 is more economical than Loan 1.