Question

You are considering the purchase of a car that costs $30,000. A local bank offers to provide financing for this purchase at a rate of 9%. You are required to make 60 monthly payments to repay this loan. Depending on when the payments start, the monthly payment will differ. You are asked to consider the three scenarios below and solve for the payment amount in each scenario.

Scenario	The first payment starts at:	Monthly Payment
I	End of the first month
II	Beginning of the first month
III	End of the third month

Additional Question assuming Scenario I	Answer
Assume that you have completed payments for 10 months, what is the remaining loan balance?

[show your calculations.]

Answer 1

Solution 1:

Scenario I: First payment at the end of first month

Loan amount = $30,000

Monthly interest rate = 9%/12 = 0.75%

Nos of monthly payments = 60

Monthly payment = Loan amount / Cumulative PV factor at 0.75% for 60 periods of ordinary annuity

= $30,000 / 48.17337 = $622.75

Scenario II: First payment at the Beginning of the first month

Monthly payment =

Loan amount / Cumulative PV factor at 0.75% for 60 periods of annuity due

= $30,000 / 48.53467 = $618.11

Scenario III: First payment at the end of the third month

Monthly payment =

Loan amount / Cumulative PV factor at 0.75% for 3rd period to 62th period of ordinary annuity

= $30,000 / 47.45882 = $632.13

Solution 2:

Loan balance = Present value of monthly payment at the end of 10th month for remaining installments

= $622.75 * Cumulative PV Factor at 0.75% for 50 periods

= $622.75 * 41.56645 = $25,885.50