John-Freddi bought a Mercedes when he came to Tech as an engineering student (so

Question

John-Freddi bought a Mercedes when he came to Tech as an engineering student (so that his fee would not get cold 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 16% per year with quarterly compounding. After four years at the time that John- Freddi made his 16th payment, he got married (too many dates!) and sold the Mercedes to his buddy Sam. Sam made arrangements with John-Freddi's bank to refinance the loan and to pay John-Freddi unpaid balance by making 16 equal quarterly payments at the same interest rate that John-Freddi was paying. After 3 years, at the time that Sam made his 12th payment, Sam flunked out (too many dates!) and sold the car to Rosa. Rosa paid the bank $4,000 cash (she had a good summer job!) to pay the loan balance. What was the amount of John-Freddi's loan to purchase the Mercedes when it was new?

Explanation / Answer

Assumed Original loan was $100 Principal 100 Interest 4% per quarter N period 20 Instalmment $            7.36 Monthly Mortgage Payment= =(100*4%*(1+4%)^20)/((1+4%)^20-1)           7.3582 Loan Balance After 16th Instalment 17 th interest and principal payment total Instalment              20.00 Less: Already paid (17-1)              16.00 Remaining Instalment (t)                 4.00 Quaterly Payment (PMT)                 7.36 Quaterly Rate of Interest ( r ) 4.0000% PV=PMT*(1-(1+r)/t)/r =7.3582*(1-(1+4%)^-4)/4%          26.7094 Principal          26.7094 Interest 4% per quarter N period 16 Instalmment $            2.29 Monthly Mortgage Payment= =(26.7094*4%*(1+4%)^16)/((1+4%)^16-1)           2.2922 Loan Balance After 12th Instalment 13 th interest and principal payment total Instalment              16.00 Less: Already paid (13-1)              12.00 Remaining Instalment (t)                 4.00 Quaterly Payment (PMT)            2.2922 Quaterly Rate of Interest ( r ) 4.0000% PV=PMT*(1-(1+r)/t)/r =2.2922*(1-(1+4%)^-4)/4%            8.3204 If principal was 100 than remaining balanace was 8.3204 If principal was 1 than remain balamnce was 8.3204/100 if remaing was 4000 than principal was =4000/(8.3204/100)           48,075

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