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Question 4.T-Y-S.V: A mortgage banking company has been evaluating the merits of...

A mortgage banking company has been evaluating the merits of a 50-year mortgage (in addition to their popular 30-year mortgage). The basic idea is to reduce the monthly payment and make home ownership more affordable. The APR of either mortgage is 6 \%, and the compounding is monthly. (4.15)

a. For a mortgage loan of \$ 300,000, what is the difference in the monthly payment for the 30 -year mortgage and the 50 -year mortgage?

b. What is the difference in total interest paid between the two mortgages?

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(a) For a 30-year loan:

A=\$ 300,000(A / P, 0.5 \%, 360)=\$ 300,000(0.0060)=\$ 1,800 per month

For a 50-year loan:

A=\$ 300,000(A / P, 0.5 \%, 600)=\$ 300,000(0.0053)=\$ 1,590 per month

The difference is \$ 210 per month.

(b) 30-year: Total interest paid =\$ 1,800(360)-\$ 300,000=\$ 348,000

50-year: Total interest paid =\$ 1,590(600)-\$ 300,000=\$ 654,000

Difference =\$ 306,000

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