1 Joe Showoff bought a Mercedes when he came to Tech as an engineering student w

Question

1 Joe Showoff bought a Mercedes when he came to Tech as an engineering student would not get cord on the way to those early morning classes). The Mercedes was purchased by making a loan that was to be paid off in 20 equal. quarterly payments. The interest rate on the loan was 12% per year with quarterly compounding. After four years. at the time that Joe made his 16th payment, he got married (too many dates!) and sold the Mercedes to his buddy Sam Pledge. Sam made arrangements with Joe's bank to refinance an and to pay Joe's unpaid balance by making 16 equal quarterly payments at the same interest rate to at the time that Sam made his 13th payment, Sam flunked out (too many dates!)and sold the car to Nancy. Nancy paid the bank $2,000 cash (she had a good summer job!) to pay the loan balance What was the amount of Joe's loan to purchase the Mercedes when it was new?

Explanation / Answer

Loan Paid after 13 payment of sam = 2000

Sam Quarterly Payment =Loan Paid after 13 payment of sam / ((1-(1+r)^-n)/(r))

Sam Quarterly Payment = 2000/((1-(1+12%/4)^-3)/(12%/4))

Sam Quarterly Payment = $ 707.0607

Loan outstanding at the time joe sold mercedes = Sam Quarterly Payment* ((1-(1+r)^-n)/(r))

Loan outstanding at the time joe sold mercedes = 707.0607*((1-(1+12%/4)^-16)/(12%/4))

Loan outstanding at the time joe sold mercedes = $ 8881.46

No of Quarter outstanding for joe at the time of sale to sam = 20-16 = 4

Joe Quarterly Payment =Loan outstanding at the time joe sold mercedes/ ((1-(1+r)^-n)/(r))

Joe Quarterly Payment =8881.46/((1-(1+12%/4)^-4)/(12%/4))

Joe Quarterly Payment = 2389.353

Joe Loan Amount to purchase the mercedes = Joe Quarterly Payment *((1-(1+r)^-n)/(r))

Joe Loan Amount to purchase the mercedes = 2389.353*((1-(1+12%/4)^-20)/(12%/4))

Joe Loan Amount to purchase the mercedes = $ 35,547.55

Answer

$ 35,547.55

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