Question

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Suppose that you decide to borrow $14,000 for a new car. You can select one of the following loans, each requiring
regular monthly payments.
Installment Loan A: three-year loan at 5.1%
Installment Loan B: five-year loan at 4.8%
PA
[1-(1-+-:)]
Use PMT=
to complete parts (a) through (c) below.
a. Find the monthly payments and the total interest for Loan A.
The monthly payment for Loan A is S
(Do not round until the final answer. Then round to the nearest cent as needed.)
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Answer 1

$2,602.44

Explanation:

To find the monthly payments and the total interest for Loan A, we can use the formula for the present value of an installment loan:

PV = PMT x [1 - (1 + r/n)^(-nt)] x (n/r)

where PV is the present value of the loan, PMT is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years of the loan.

For Loan A, we have:

PV = $14,000

r = 0.051 (5.1% as a decimal)

n = 12 (monthly payments)

t = 3

Substituting these values into the formula and solving for PMT, we get:

PMT = PV / ([1 - (1 + r/n)^(-nt)] x (n/r))

= 14000 / ([1 - (1 + 0.051/12)^(-12*3)] x (12/0.051))

= $417.79

So the monthly payment for Loan A is $417.79.

To find the total interest paid over the life of the loan, we can simply multiply the monthly payment by the total number of payments and subtract the original loan amount:

Total interest = PMT x (nt) - PV

= 417.79 x (3 x 12) - 14000

= $2,602.44

Therefore, the total interest paid for Loan A is $2,602.44.