Question

Suppose that you decide to borrow ​$16,000

for a new car. You can select one of the following​ loans, each requiring regular monthly payments.
Installment Loan​ A: three-year loan at 5.9​%
Installment Loan​ B: five-year loan at 5.8%

Answer 1

To find out the monthly payments for each loan option, we can use the loan amortization formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

For Installment Loan A:
Loan Amount = $16,000
Annual Interest Rate = 5.9%
Monthly Interest Rate = 5.9% / 12 = 0.4917%
Number of Payments = 3 years * 12 months/year = 36

Monthly Payment (Installment Loan A) = (16000 * 0.4917%) / (1 - (1 + 0.4917%)^(-36))

For Installment Loan B:
Loan Amount = $16,000
Annual Interest Rate = 5.8%
Monthly Interest Rate = 5.8% / 12 = 0.4833%
Number of Payments = 5 years * 12 months/year = 60

Monthly Payment (Installment Loan B) = (16000 * 0.4833%) / (1 - (1 + 0.4833%)^(-60))

Now, we can calculate the monthly payments for each loan option:

Monthly Payment (Installment Loan A) = ($79.12)
Monthly Payment (Installment Loan B) = ($71.31)

Therefore, the monthly payment for Installment Loan A is $79.12, while the monthly payment for Installment Loan B is $71.31.