Question

Use the following to answer questions 20 - 24 On January 1, year 1, AJ borrows $41,000 to purchase a new vehicle by agreeing to a 4.0%, 6-year loan with the bank. Payments are due at the end of each month with the first installment (vehicle payment) due on January 31, year 1. After completing the problem, ROUND YOUR ANSWERS TO THE NEAREST DOLLAR. IMPORTANT!!!! when inputting the monthly interest rate DO NOT ROUND IT (use the math function in the spreadsheet/financial calculator). 20. Determine the monthly vehicle payment (installment) $_ 21. Determine the interest expense for the first car payment $_ 22. How much of the payment will decrease the amount owed (principal)? $_ 23. After the first vehicle payment is made the amount owed on the vehicle would be: $_ 24. Determine interest expense for the second car payment $.

Answer 1

Answer 20:

Amount Borrowed = $41,000
Annual Interest Rate = 4.00%
Monthly Interest Rate = 0.3333%
Period = 6 years or 72 months

Let Monthly Payment be $x

$41,000 = $x/1.003333 + $x/1.003333^2 + … + $x/1.003333^71 + $x/1.003333^72
$41,000 = $x * (1 - (1/1.003333)^72) / 0.003333
$41,000 = $x * 63.9181814
$x = $641

Monthly Payment = $641

Answer 21-24:

First Payment:

Beginning Loan Outstanding = $41,000

Interest Expense = $41,000 * 0.3333%
Interest Expense = $137

Principal Repaid = $641 - $137
Principal Repaid = $504

Ending Loan Outstanding = $41,000 - $504
Ending Loan Outstanding = $40,496

Second Payment:

Beginning Loan Outstanding = $40,496

Interest Expense = $40,496 * 0.3333%
Interest Expense = $135