Question

A family has a $150,000, 30-year mortgage at 6.1% com-pounded monthly.

Answer 1

Answer:

Monthly payment = $908.99

(A) $125,862.32

Step-by-step explanation:

Given:

Present value = $150,000

Duration, n = 30 years = 30 × 12 = 360 months

Interest = 6.1% compounded monthly

or

Monthly interest, r = $\frac{\textup{6.1}}{\textup{12}}$ =  0.5083%

Now,

Monthly payments can be calculated using the formula

$\textup{Present value}=\textup{Monthy payment}\times(\frac{1-(1+r)^{-n}}{r})$

thus,

$\ \textup{150,000}=\textup{Monthy payment}\times(\frac{1-(1+0.005083)^{-360}}{0.005083})$

or

Monthly payment = $908.99

(A) unpaid balance after 10 years will be equal to the payment made in 20 years starting from the end of 10th year

thus,

n = 20 × 12 = 240

Unpaid balance = $\textup{Monthy payment}\times(\frac{1-(1+r)^{-n}}{r})$

or

Unpaid balance = $\textup{908.99}\times(\frac{1-(1+0.005083)^{-240}}{0.005083})$

or

Unpaid balance after 10 years = $125,862.32