Question

-both loans afe fixed rate and have the same closing costs

Compare the monthly payments and total loan costs for the following pairs of loan options You need a $30,000 loan. Option 1: a 30-year loan at an APR of 6.65%. Option 2: a 15-year loan at an APR of 6.25%. The monthly payment for option 1 is $ . The monthly payment for option 2 is $|| (Do not round until the final answer. Then round to the nearest cent as needed.) Find the total amount paid for each option. The total payment for option 1 is $ The total payment for option 2 is $ (Use the answers from the previous step. Round to the nearest cent as needed.) Compare the two options to determine which is the better economic option. Which appears O A. Option 1 is the better option, but only if the borrower needs the lower monthly paym O B. Option 2 is the better option, but only if the borrower can afford the higher monthly c. Option 2 will always be the better option. OD. Option 1 will always be the better option

Answer 1

Answer-

Loan amount = $ 30000

Option 1
Interest rate ( APR) = 6.65 % = 6.65 % / 12 = 0.554 % / month
Number of years = 30
number of monthly payments = 30 x 12 = 360

The monthly payment in Option 1 :

PV = $ 30000
N = 360
I / Y = 0.554
FV = 0
PMT = $ 192.55
Therefore the monthly payment for Option 1 = $ 192.55

Option 2
Interest rate ( APR) = 6.25 % = 6.25 % / 12 = 0.521 % / month
Number of years = 15
number of monthly payments = 15 x 12 = 180

The monthly payment in Option 1 :

PV = $ 30000
N = 180
I / Y = 0.521
FV = 0
PMT = $ 257.26

Therefore the monthly payment for Option 2 = $ 257.26

The total payment for Option 1 is
= monthly payment x number of payments
= $ 192.55 x 360
= $ 69318

The total payment for Option 2 is
= monthly payment x number of payments
= $ 257.26 x 180
= $ 46306.8

Comparison of two options in terms of economic value

Answer - The second choice B is correct .

Option 2 is the better option but only if the borrower can afford the higher monthly payments over the entire term of loan. For option 2 the interest rate is lower than option 1 (0.521 < 0.554 ) and there is lot of difference in the total amount paid for a loan of $ 30000 ( $ 69318 - $ 46306.8 = $ 23011.2) . One can save $ 23011.2 in option 2 though the monthly payments are high ( $ 257.26 > $ 192.55) .