Question

If Sandy can afford car payments of

​$440

per month for

5

​years, what is the price of a car that she can afford​ now? Assume an interest rate of

7.8

percent.

Answer 1

Here, the payments will be same every month, so it is an annuity. We need to calculate the present value of annuity here. We will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $440, r is the rate of interest =7.8% compounded monthly, so monthly rate = 7.8% / 12 = 0.65% and n is the time period = 5 * 12 = 60 months

Now, putting these values in the above formula, we get,

PVA = $440 * (1 - (1 + 0.65%)^-60 / 0.65%)

PVA = $440 * (1 - ( 1+ 0.0065)^-60 / 0.0065)

PVA = $440 * (1 - ( 1.0065)^-60 / 0.0065)

PVA = $440 * (1 - 0.67791188279) / 0.0065)

PVA = $440 * (0.3220881172 / 0.0065)

PVA = $440 * 49.55201

PVA = $21802.89

So, price of the car is $21802.89.