0 points John-Freddi bought a Mer ercedes would not get cold on the way to those

Question

0 points John-Freddi bought a Mer ercedes would not get cold on the way to those early mornig hm as an engineering student (so that his feet urchased by The interest rate on the at the time that John- he car loan was 16% buddy Sam. S out (too many da classes). The Mercedes wa at was to be paid off in 20 equal, quarterly paymen per year with quarterly compounding. After four year is 16th payment, he got married (too many dates!) a and sold the Mercedes to his Freddi's bank to refinance the loan and to pay am made arrangements with Ereddi unpaid balance by making 16 equal quarterly paymer nis 12th payme ban nked was paying. After 3 years, at the time that Sam ma old the car to Rosa. Rosa paid the bank $4,000 cash (she had a good nce. What was the amount of John-Freddi's loan to purchase de his 12th payment, Sam u summer job!) to pay the loan the Mercedes when it was new? was the

Explanation / Answer

If we work out this question in no interest rate regime then it would work like below

Rosa paid last 4 EMIS with balance 4000 that is Sam paid 12 EMIs which will total to 12000 if we add them we get 16000 as a balance when John sold his car to Sam when his 4 EMIS were left now these 4 EMIs equal to 16000 and healredy paid 16 such EMIs which will be equal to 64000 therefore the sum equals to 80000 that is the cost of car if no interest rate assumed.

Let's work out this problem backwards,

We have 4000 left for 4 EMIs and Rosa paid it beforehand hence no interest to be paid on these.

Now we know 16000 was the principal when Sam converted it into another 16 EMIs with 16% interest rate (1+0.16/4)^4= 1.1698 that is 16.98% if compounded quarterly therefore sum to be paid in a year is 4000*1.1698=4679.2

4679.2*3= 14037.6 Sam paid through EMIs

Likewise 64000 amount was converted into 4 years EMI to be paid quarterly of 20 EMIs

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