Suppose that you decide to borrow ​$16 comma 000

Question

for a new car. You can select one of the following​ loans, each requiring regular monthly payments.
Installment Loan​ A: three-year loan at 5.9
​%
Installment Loan​ B: five-year loan at 5.8
Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction

to complete parts​ (a) through​ (c) below.
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Part 1

Answer 1

To compare the two loans, we need to calculate the monthly payments for each loan.

For Loan A, the interest rate is 5.9% per year and the loan term is 3 years. Using the PMT formula, we can calculate the monthly payment:

PMT = P * r / (1 - (1 + r)^(-nt))

where P is the loan amount, r is the interest rate per period, n is the number of periods per year, and t is the total number of years.

P = $16,000
r = 0.059 (5.9%)
n = 12 (number of months in a year)
t = 3

PMT(A) = 16000 * 0.059 / (1 - (1 + 0.059)^(-12*3))

For Loan B, the interest rate is 5.8% per year and the loan term is 5 years. Using the same formula, we can calculate the monthly payment:

PMT(B) = 16000 * 0.058 / (1 - (1 + 0.058)^(-12*5))

Now we can calculate the monthly payments:

PMT(A) = $484.32 (approximately)
PMT(B) = $316.21 (approximately)

Part 1: The monthly payment for Loan A is approximately $484.32, and the monthly payment for Loan B is approximately $316.21.