Question

# Answer these 2 separate questions: 1) You want to buy a new sports car from Muscle...

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?

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 %

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