Question

Hailey is considering taking out an 8-year loan with monthly payments of $115 at an APR of 3.2%, compounded monthly, and this equates to a loan of $9728.75. Assuming that Hailey's monthly payment and the APR of the loan remain fixed, which of these is a correct statement?

A. If it were a 6-year loan, the amount of the loan that Hailey is considering taking out would be more than $9728.75.
B. If it were a 14-year loan, the amount of the loan that Hailey is considering taking out would be less than $9728.75.
C. If it were a 12-year loan, the amount of the loan that Hailey is considering taking out would be less than $9728.75.
D. If it were a 10-year loan, the amount of the loan that Hailey is considering taking out would be more than $9728.75.

Answer 1

Let initial amount of loan = $ x

Total amount that Hailey,is thinking about taking as loan= $ 9728.75

Number of months in 8 years = 12 × 8 =96 months

So, If monthly payment= $ 115

Total money paid after 96 months = 115 × 96=$ 11040

Monthly amount if APR= 3.2 % monthly of amount x=
`(3.2 x)/(100)`

Total money paid after 6 years= 72 months = 115 × 72=$ 8280

Total money paid after 10 years= 120 months = 115 × 120=$ 13,800

Option (D) : →→ If it were a 10-year loan, the amount of the loan that Hailey is considering taking out would be more than $9728.75 is true.