Suppose that you decide to borrow ​$15,000

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 5.5%
Installment Loan​ B: five-year loan at 5.2​%
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.

Answer 1

a) Installment Loan A:

Plug the given values into the payment formula:
P = 15,000
r = 5.5/100 = 0.055 (always convert to decimal)
n = 12 (monthly payments in a year)
t = 3 years

The formula for the monthly payment (PMT) is:

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

PMT = [15000 * (0.055/12)] / [1 - (1 + 0.055/12)^-(12*3)]

PMT = [15000 * 0.00458333] / [1 - (1.004583)^-36]

PMT = 68.75 / [1 - 0.77951567]

PMT = 68.75 / 0.22048433

PMT = $311.97

You need to pay $311.97 per month for a three-year loan at 5.5%.

b) Installment Loan B:

Plug the given values into the payment formula:
P = 15,000
r = 5.2/100 = 0.052 (always convert to decimal)
n = 12 (monthly payments in a year)
t = 5 years

The formula for the monthly payment (PMT) is:

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

PMT = [15000 * (0.052/12)] / [1 - (1 + 0.052/12)^-(12*5)]

PMT = [15000 * (0.00433333)] / [1 - (1.004333)^-60]

PMT = 65.00 / [1 - 0.610772]

PMT = 65.00 / 0.389228

PMT = $167.11

You need to pay $167.11 per month for a five-year loan at 5.2%.

c) Comparison between Loans A & B:

Loan A has higher monthly payments ($311.97) but you pay off the loan faster (3 years), while Loan B has lower monthly payments ($167.11) but the loan term is longer (5 years). It depends on your monthly budget to afford the installments and how quickly you want to pay off the loan.