I am having trouble with getti g the correct I value. Can I get an explanation of how to work through the formula using this formula.

Question

Fritz Benjamin buys a car costing $15800. He agrees to make payments at the end of each monthly period for

8 years. He pays 9.6% ​interest, compounded monthly. What is the amount of each​ payment? Find the total amount of interest Fritz will pay.

Answer 1

So firstly, let us identify the type of problem this is. We may see that it is a series of monthly payments starting at the end of the month, so it must be an ordinary annuity formula (this is the case with loans such as cars, mortgages, etc.)

Okay, now that we've determined the type of problem that it is, let us determine the inputs for the problem:

1. # of periods = years × months = 8 × 12 = 96
2. PV = $15,800
3. The rate. Since these loans are usually expressed as an APR, we may find it the following way:

APR = r × m

r = APR/m = 9.6%/12 = 0.8%

We know that for an ordinary annuity, PV = (c/r) × [1-(1/(1+r)^t)]. We should try to isolate c in this case.

PV × r = c × [1-(1/(1+r)^t)]

c = (PV × r)/[1-(1/(1+r)^t)]

c = ($15,800 × .008)/[1-(1/(1+.008)^96)]

c = $236.42

Thus, Fritz makes a payment of $236.42 monthly for 8 years.