Answer
It is more economical to have a 20-year mortgage at a rate of 7.5%. The amount of interest that is saved is $\$106,440$.
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%.
$PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$
$PMT = \frac{(\$150,000)~(\frac{0.08}{12})}{[1-(1+\frac{0.08}{12})^{-(12)(30)}~]}$
$PMT = \$1101$
The monthly payments are $\$1101$
We can find the total amount paid.
$\$1101 \times 360 = \$396,360$
The interest is the difference between the total amount paid and the price of the home.
$I = \$396,360 - \$150,000 = \$246,360$
The interest is $\$246,300$
We can calculate the monthly payments for a 20-year mortgage at 7.5%.
$PMT = \frac{P~(\frac{r}{n})}{[1-(1+\frac{r}{n})^{-nt}~]}$
$PMT = \frac{(\$150,000)~(\frac{0.075}{12})}{[1-(1+\frac{0.075}{12})^{-(12)(20)}~]}$
$PMT = \$1208$
The monthly payments are $\$1208$
We can find the total amount paid.
$\$1208 \times 240 = \$289,920$
The interest is the difference between the total amount paid and the price of the home.
$I = \$289,920 - \$150,000 = \$139,920$
The interest is $\$139,920$
We can calculate the difference in interest paid.
$\$246,360-\$139,920 = \$106,440$
It is more economical to have a 20-year mortgage at a rate of 7.5%. The amount of interest that is saved is $\$106,440$
