Answer
It is more economical to have a 15-year mortgage at a rate of 7.5%. The amount of interest that is saved is $\$87,480$.
Work Step by Step
We can use this formula to calculate the payments for a mortgage:
$PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$
$PMT$ is the amount of the regular payment
$P$ is the price of the home
$r$ is the interest rate
$n$ is the number of payments per year
$t$ is the number of years
We can calculate the monthly payments for a 30-year mortgage at 8%.
$PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$
$PMT = \frac{(\$90,000)~(\frac{0.08}{12})}{[1-(1+\frac{0.08}{12})^{-(12)(30)}~]}$
$PMT = \$660$
The monthly payments are $\$660$
We can find the total amount paid.
$\$660 \times 360 = \$237,600$
The interest is the difference between the total amount paid and the price of the home.
$I = \$237,600 - \$90,000 = \$147,600$
The interest is $\$147,600$
We can calculate the monthly payments for a 15-year mortgage at 7.5%.
$PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$
$PMT = \frac{(\$90,000)~(\frac{0.075}{12})}{[1-(1+\frac{0.075}{12})^{-(12)(15)}~]}$
$PMT = \$834$
The monthly payments are $\$834$
We can find the total amount paid.
$\$834 \times 180 = \$150,120$
The interest is the difference between the total amount paid and the price of the home.
$I = \$150,120 - \$90,000 = \$60,120$
The interest is $\$60,120$
We can calculate the difference in interest paid.
$\$147,600-\$60,120 = \$87,480$
It is more economical to have a 15-year mortgage at a rate of 7.5%. The amount of interest that is saved is $\$87,480$
