15. If the interest rate on a 20-year mortgage for $275,000 were changed from 3.4% to 2.9%, how much would you save over the life of the loan?

The total payment made for a mortgage is :
[tex]T=Pn\times\frac{r(1+r)^n}{(1+r)^n-1}[/tex]where T is the total payment made
P is the financed amount
r is the monthly interest rate, annual rate divided by 12
n is the number of payments
From the problem :
P = $275,000
r1 = 3.4% or 0.034/12
n = 20 years x 12 months = 240 months
Using the formula above, the total payment made for 3.4% rate is :
[tex]\begin{gathered} T=275000(240)\times\frac{\frac{0.034}{12}(1+\frac{0.034}{12})^{240}}{(1+\frac{0.034}{12})^{240}-1} \\ T=379390.6462 \end{gathered}[/tex]Using the same formula but with r2 = 2.9% rate, the total payment is :
[tex]\begin{gathered} T=275000(240)\times\frac{\frac{0.029}{12}(1+\frac{0.029}{12})^{240}}{(1+\frac{0.029}{12})^{240}-1} \\ T=362739.2992 \end{gathered}[/tex]The difference is :
379390.6462 - 362739.2992 = $16,651.347
You will save $16,651.35