Respuesta :
The formula to calculate the mortgage payment is as follows:
[tex]M=P\frac{\lbrack i(1+i)^n\rbrack}{\lbrack(1+i)^n-1\rbrack}[/tex]Where P is the principal loan amount $325,000
i is the monthly interest rate, divide the annual interest rate by 12 to find the monthly interest rate.
n is the number of payments over the lifetime of the loan (months) then as you have a 30-year mortgage n=30 years x 12 months per year=360 payment months.
a. For 2.9% interest rate:
i=2.9%/12=0.029/12=0.002417
Replace the known values:
[tex]\begin{gathered} M1=325,000\frac{\lbrack0.002417(1+0.002417)^{360}\rbrack}{\lbrack(1+0.002417)^{360}-1\rbrack} \\ M1=325,000\frac{\lbrack0.002417\cdot2.38441\rbrack}{\lbrack2.38441-1\rbrack} \\ M1=325,000\frac{0.005762}{1.38441} \\ M1=1352.75 \end{gathered}[/tex]This would be the monthly payment when interest rate is 2.9%
b. For 2.6% interest rate:
i=2.6%/12=0.026/12=0.002167.
[tex]\begin{gathered} M2=325,000\frac{\lbrack0.002167(1+0.002167)^{360}\rbrack}{\lbrack(1+0.002167)^{360}-1\rbrack} \\ M2=325,000\frac{\lbrack0.002167\cdot2.17963\rbrack}{\lbrack2.17963-1\rbrack} \\ M2=325,000\frac{0.004723}{1.17963} \\ M2=1301.1 \end{gathered}[/tex]Thus, to calculate how much would you save over the life of the loan, multiply each monthly payment by 360 payments, and the difference would be the money you save:
[tex]\begin{gathered} At\text{ 2.9\% interest rate:} \\ 1352.75\times360=486989.1 \\ At\text{ 2.6\% interest rate:} \\ 1301.1\times360=468397.5 \\ \text{Money saved: }486989.1-468397.5=18591.6 \end{gathered}[/tex]Answer: You save $18591.6 over the life of the loan if the interest changed from 2.9% to 2.6%
