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 ​$110,000 loan.

Option​ 1: a​ 30-year loan at an APR of 7.25​%.

Option​ 2: a​ 15-year loan at an APR of 6.8%.

1.) Find the monthly payment for each option.

The monthly payment for option 1 is what?

The monthly payment for option 2 is​ what?.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

2.) Find the total payment for each option.

The total payment for option 1 is what?

The total payment for option 2 is what?

​(Round to the nearest cent as​ needed.)

Compare the two options. Which appears to be the better​ option?

A.Option 2 is the better​ option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.

B.Option 1 will always be the better option.

C.Option 1 is the better​ option, but only if the borrower plans to stay in the same home for the entire term of the loan.

D.Option 2 will always be the better option

Answer 1

Solution :

Loan = $110,000

Option 1

n = 30 years adjust for monthly compounding = 30*12 = 360

APR = 7.25% adjust for monthly compounding

r =0.0725/12 =0. 0060417

Calculate the monthly payments

Total loan cost = Total payments - Loan

Total loan cost = (750.387*360) - 110,000

Total loan cost =$ 160,139.32

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Option 2

n = 15 years adjust for monthly compounding 15*12 =180

APR = 6.8% adjust for monthly compounding

r =0.068/12=0.005667

Calculate the monthly payments

Total loan cost = Total payments - Loan

Total loan cost = (976.47 * 180) - 110,000

Total loan cost =$ 65,764.6

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Comparing the two options :

1.The monthly payments of option 1 < monthly payments of option-2. Option 1 has a longer loan term and a higher interest rate compared to option-2.

2. The total cost of option-1 is much higher than the cost of option-2

Therefore, (A) is correct answer.

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