Question

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?

Answer 1

The total payment made for a mortgage is :

$T=Pn\times\frac{r(1+r)^n}{(1+r)^n-1}$

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 :

$\begin{gathered} T=275000(240)\times\frac{\frac{0.034}{12}(1+\frac{0.034}{12})^{240}}{(1+\frac{0.034}{12})^{240}-1} \\ T=379390.6462 \end{gathered}$

Using the same formula but with r2 = 2.9% rate, the total payment is :

$\begin{gathered} T=275000(240)\times\frac{\frac{0.029}{12}(1+\frac{0.029}{12})^{240}}{(1+\frac{0.029}{12})^{240}-1} \\ T=362739.2992 \end{gathered}$

The difference is :

379390.6462 - 362739.2992 = $16,651.347

You will save $16,651.35