Car payments are determined using simple interest. If you don’t remember this fo

Question

Car payments are determined using simple interest. If you don’t remember this formula, go back and look it up! To finance your vehicle purchase you have two choices. Write two equations, one for each bank, that models the banks' loan options using x for the price of the vehicle and y to represent the total cost (price, interest and origination fees) paid on each loan. Be sure to label which equation goes with which bank.

Bank A: Finance the full price of the vehicle at 5% with an origination fee of $200 paid over 5 years.

Bank B: Finance the full price of the vehicle at 4.5% paid over 6 years (no additional fees).

Explanation / Answer

Let $ P be the amount of loan taken in cases of both the Bank A and Bank B and let $ X be the monthly installment.

For the Bank A, there is an origination fee of $ 200, so the amount of loan becomes$ ( P+200). The interest on this amount at 5 % for 5 years is (P+200) *(5/100)*5 = ¼(P+200) = (P/4)+50. Then X = (Principal +interest)/No. of months = [P + (P/4)+50 ]/60 or,   X = [(5P/4)+50]/60.

For Bank B, the amount of interest is P *(4.5/100)*6 = 0.27P. Then X = (P+0.27P)/72 = 1.27P/72

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