Question

Determine the monthly principal and interest payment for a 20-yearmortgage when the amount financed is $255,000 and the annualpercentage rate (APR) is 5.0%.The monthly principal and interest payment is $(Round to the nearest cent as needed.)

Answer 1

The general formulae for the monthly payment for the mortgage is given by

$\begin{gathered} M\text{ =}P\lbrack\frac{r(1+r)^n}{(1+r)^n-1}\rbrack\text{ where} \\ M\text{ = monthly payments} \\ P\text{ = Principal loan amount}=255,000 \\ r=\text{interest rate}=\frac{5}{100}=0.05 \\ n=no\text{ of payment over loan's lifetime}=12\times20=240 \end{gathered}$

Substituting, we get:

$M=255000\lbrack\frac{0.05(1+0.05)^{240}}{(1+0.05)^{240}-1}\rbrack=12,750.1047$

Therefore, Monthly Payment = $12,750.10

The interest payment will be gotten with the formulae below:

$\begin{gathered} i=P(\frac{r}{n_y})\text{ where} \\ n_y=no\text{ of payments per year} \\ i=255000\times\frac{0.05}{12}=1062.5 \end{gathered}$

i = $1062.50