Question

you are borrowing $6500 to purchase a car.  However, now the first payment is due immediately.  There will be a total of 36 monthly payments (The first payment occurs immediately.   The remaining 35 occur at the end of each of the following months growing by 2% per month).  use an interest rate of r = 0%.    Then answer the following questions:

Part A)   What is the size of the 6th (sixth) payment?   

    Hint:  The answer is not $140.79

Answer 1

Trick of the question lies in timing of the payment. Let each time period be 1 month ie t=1 mean end of month 1, t=2 mean end of month 2 and so on...

Here, first payment is made on t = 0. Let it be called X.

Then as next payment is made at the end of following month. Hence, there would be no payment at t=1. The next payment will be at t=2. And then we will have one made for 35 periods ie till t=36.

So, payment at t=2 will be X * (1.02)^2, payment at t=3 will be X * (1.02^3) and so on...

Present value of the geometric progression series starting from t= 2 will be:

X*(1.02)^2 *((1.02^35 - 1)/(1.02 -1))

Hence, total outflow of money = X + Payment from t=2 = X + X*(1.02)^2 *((1.02^35 - 1)/(1.02 -1)) = Total Inflow of money = $6,500

On solving the above equation, we get X = $122.608

Hence, we get 6th payout as payout in t=7 as X*(1.02^7) which is $140.84