Christine bought a BMW when she came to LA as a County Judge. The BMW was purcha

Question

Christine bought a BMW when she came to LA as a County Judge. The BMW was purchased by taking 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 Christine made her 16th payment, she got married and sold the BMW to her friend Jane. Jane made arrangements with Christine's bank to refinance the loan and to pay Christine's unpaid balance by making 16 equal quarterly payments at the same interest rate that Christine was paying. After 3ݼ years, at the time that Jane made her 13th payment, Jane flunked out and sold the car to Ally. Ally paid the bank $3,000 cash to pay the loan balance. What was the amount of Christine's loan to purchase the BMW when it was new?

Explanation / Answer

i = 12/4 = 3%

christine W.

A = P(A/P, 3%, 20)

A = P(.0672) Quarterly payment for christine

christine owes

P = .0672P(P/A, 3%, 4) Present worth of four remaining payments

= .0672P(3.717)

= .2498P

jane S.

A = .2498P(A/P, 3%, 16) Quarterly payment for jane

= .2498P(.0796)

= .0199P

ally M.

P = .0199P(P/A, 3%, 3) Present worth of three remaining payments

= .0199P(2.829)

= .0563P

Set final payment equal to present worth of remaining payments

3000 = .0562P

P = $53380.78

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