Suppose that you decide to borrow $16 comma 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
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
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.
To complete part 1, we need to calculate the regular monthly payments for each loan option.
For Loan A, we have a three-year loan at 5.9% interest.
Using the formula PMT = P * ((r/n) / (1 - (1 + (r/n))^(-n*t))), where:
P = principal amount borrowed = $16,000
r = annual interest rate = 5.9% = 0.059
n = number of compounding periods per year (monthly payments) = 12
t = total number of years = 3
PMT_A = $16,000 * ((0.059/12) / (1 - (1 + (0.059/12))^(-12*3)))
For Loan B, we have a five-year loan at 5.8% interest.
Using the same formula with different values:
P = $16,000
r = 5.8% = 0.058
n = 12
t = 5
PMT_B = $16,000 * ((0.058/12) / (1 - (1 + (0.058/12))^(-12*5)))
Now we can calculate the values of PMT_A and PMT_B.