Question

A family has a $142,847, 25-year mortgage at 4.8% compounded monthly (A) Find the monthly payment and the total interest paid. (B) Suppose the family decides to add an extra $100 to its mortgage payment each month starting with the very first payment. How long will it take the family to pay off the mortgage? How much interest will the family save? (A) Monthly payment: $ (Round to two decimal places.)

Answer 1

(A)

The monthly interest must be 4.8% / 12 = 0.4%.

The monthly payment is calculated below:

$142,847=Monthly\, payment\times \left ( \frac{1-\left ( 1+0.004 \right )^{-300}}{0.004} \right )$

$142,847=Monthly\, payment\times 174.52$

The total interest paid is calculated below:

300 x 818.51 – 142, 847 Total interest

Total interest = 102, 705.69

(B)
The time taken to pay off the loan is calculated below:

$142,847=918.51\times \left ( \frac{1-\left ( 1+0.004 \right )^{-n}}{0.004} \right )$

$155.52= \left ( \frac{1-\left ( 1+0.004 \right )^{-n}}{0.004} \right )$

$0.62208= 1-\left ( 1+0.004 \right )^{-n}$

$\left ( 1+0.004 \right )^{-n}=0.3779$

taking log on both sides

$-nlog\left ( 1+0.004 \right )=log\left (0.3779 \right )$

$-n=-243.75$

There will be total 244 months needed to pay off the loan, that is, 20.33 years.

Interest saved is calculated below:

$Interest saved=102,705.69-\left (244\times 918.51-142,847 \right )$