Question

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a ​$90,000 loan.

Calculate

Option​ 1: a​ 30-year loan at an APR of 6.65​%.

Option​ 2: a​ 15-year loan at an APR of 6.25%.

Answer 1

Option 1

This is the information we have been provided with:

The amount of the loan (principal) is: L=90000, the APR is r=0.0665, and the term is for n=30 years.

Therefore, effective monthly rate is

and the monthly payment is computed using the following formula:

Therefore, the monthly mortgage payment for a loan (principal) of L=90000, and APR r=0.0665, and a loan term of n=30 years is $577.77

Total loan cost = 577.77*12*30 = 207997.2

Total interest paid = 207997.2 - 90000 = $117997.2

OPTION 2

This is the information we have been provided with:

The amount of the loan (principal) is: L=90000, the annual nominal rate r=0.0625, and the term is for n=15 years.

Therefore, effective monthly rate is ,

and the monthly payment is computed using the following formula:

Therefore, the monthly mortgage payment for a loan (principal) of L=90000, and APR r=0.0625, and a loan term of n=15 years is $771.68.

Total loan cost = 771.68*12*15 = 138902.4

Total interest paid = 138902.4- 90000 = 48902.4

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