(Question and Answer): You have your eyes on a new automobile costing $25,000. If you had the $25,000 and wrote a check for that a

6. You have your eyes on a new automobile costing $25,000. If you had the $25,000 and wrote a check for that amount, you could drive off the car lot in your new car. But, you dont have it. Not to worry, says the salesperson. We can finance it! You have $5,000 available and wish to finance $20,000. The dealers rate is 15% per annum compounded monthly or 15% year/ th and the dealer is ling to help you out by financing it over a 5-year period to keep the monthly payments smaller. The dealer proceeds to add on at 25% loan initiation fee of $250. Also, there is a prepaid loan closeout fee of another $250. Then there is the paperwork filing and storage fee of $100 and a prepaid loan maintenance fee of only $8/month or $480 for the 60-month loan. At this point, the dealer is talking rather quickly and your head is spinning. You are assured that these smaller fees are required and routine. However, you should not be concerned because they can all be rolled into your loan. The dealer adds up the dollars for you: $20,000 $250 $250 $100 + $480 $21,080 He then calculates the loan payment using Excel -PMT 1.25%,60 21080-$501.49 a) What is the monthly rate of interest you are really paying for the $20,000 loan? (10 pts) b) c) What is the nominal annual interest rate you are really paying for the $20,000 loan? (10 pts) What is the effective annual interest rate you are really paying for the $20,000 loan? (10 pts)

You have your eyes on a new automobile costing $25,000. If you had the $25,000 and wrote a check for that amount, you could drive off the car lot in your new car. But, you don’t have it. ‘Not to worry,” says the salesperson. “We can finance it!” You have $5,000 available and wish to finance $20,000. The dealer’s rate is 15% per annum compounded monthly or 15%/year/month and the dealer is willing to help you out by financing it over a 5-year period to keep the monthly payments smaller. The dealer proceeds to add on a1.25% loan initiation fee of $250. Also, there is a prepaid loan closeout fee of another $250. Then there is the paperwork filing and storage fee of $100 and a prepaid loan maintenance fee of only $8/month or $480 for the 60-month loan. At this point, the dealer is talking rather quickly and your head is spinning. You are assured that these smaller fees are required and routine. However, you should not be concerned because they can all be rolled into your loan. The dealer adds up the dollars for you. $20,000 + $250 + $250 + $100 + $480 = $21,080. He then calculates the loan payment using Excel: =PMT(1.25%,60,-21080) = $501.49. a) What is the monthly rate of “interest’ you arc really paying for the $20,000 loan? b) What is the nominal annual “interest” rate you are really paying for the $20,000 loan? c) What is the effective annual “interest” rate you are really paying for the $20,000 loan?

Expert Answer

 

a) The monthly rate of interest is calculated as follows

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PMT = Present value of loan div 1 – [ 1 + (r/12) ] 60/ r

$ 501.49 = $ 20,000div 1 – [ 1 + (r/12) ] 60/ r

solving for r

Monthly rate of interest = 1.45 %

____________________________________________________________________________

b) The nominal rate of interest = 1.45% * 12

Nominal rate of interest = 17.41%

________________________________________________________________________________

C) Effective rate of interest = [ 1 + ( 0.1741/12) ]12 x 1 – 1

Effective rate of interest = 18.87 %

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