You borrow $26,500 to purchase a brand new car. The interest rate is 6%, and the...

You borrow $26,500 to purchase a brand new car. The interest rate is 6%, and the dealer says that you can pick between a 4-year or 6-year loan. How much more interest would you have to pay on your loan if you selected the 6-year loan over the 4-year loan.

Expert Solution

Step 1 - Calculation of total interest paid for 6 year Loan
We can use the present value of annuity formula to calculate the monthly loan payment.
Present Value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan amount = $26500
P = monthly loan payment = ?
r = interest rate per month = 6%/12 = 0.005
n = number of monthly loan payments = 6 years x 12 = 72
26500 = P x {[1 - (1+0.005)^-72]/0.005}
26500 = P x 60.33951
P = 439.18
Monthly Loan payment = $439.18
Total Interest paid for 6 year loan = (Monthly loan payment x number of monthly payments) - Loan amount
Total Interest paid for 6 year loan = ($439.18 x 72) - $26,500
Total Interest paid for 6 year loan = $31,621.07 - $26,500
Total Interest paid for 6 year loan = $5,121.07

Step 2 - Calculation of total interest paid for 4 year Loan
We can use the present value of annuity formula to calculate the monthly loan payment.
Present Value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan amount = $26500
P = monthly loan payment = ?
r = interest rate per month = 6%/12 = 0.005
n = number of monthly loan payments = 4 years x 12 = 48
26500 = P x {[1 - (1+0.005)^-48]/0.005}
26500 = P x 42.58032
P = 632.35
Monthly Loan payment = $632.35
Total Interest paid for 4 year loan = (Monthly loan payment x number of monthly payments) - Loan amount
Total Interest paid for 4 year loan = ($632.35 x 48) - $26,500
Total Interest paid for 4 year loan = $29,872.96 - $26,500
Total Interest paid for 4 year loan = $3,372.96

More amount of Interest paid on your loan if you selected the 6-year loan over the 4-year loan = $5,121.07 - $3,372.96
More amount of Interest paid on your loan if you selected the 6-year loan over the 4-year loan = $1,748.11

jeff jeffy answered 1 year ago

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