Question

Answer these 2 separate questions:

1)

You want to buy a new sports car from Muscle Motors for $36,000. The contract is in the form of a 72-month annuity due at a 6.50 percent APR.

  

Required:

What will your monthly payment be?

2)

You are looking at a one-year loan of $15,000. The interest rate is quoted as 9 percent plus 3 points. A pointon a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay 3 points to the lender up front and repay the loan later with 9 percent interest.

  

Required :

What rate would you actually be paying here?

Answer 1

1) We will use

PVA due equation i.e. :

PVAdue = (1 + r) PVA

PVAdue = $36,000 = [1 + (.065 / 12)] × C[{1 – 1 / [1 + (.065 / 12)]72} / (.065 / 12)]

C = $ 605.16 ( by using the formula ) 2 ) Loan repayment amount = $15,000(1.09) = $ 16,350 The amount we will receive today is the principal amount of the loan times one minus the points: Amount received = $15,000 (1- .03 ) = $ 14,550 Now, we need to find the interest rate for this PV and FV. FV=PV±(1 +r)t $16,350 = $14,550(1 +r)1 ( 1 + r ) = $ 16350/ $ 14550 r = 1.12371- 1= 0.12371= 12.32 %