Compounded Monthly

[rosy_peach]

Jeffrey purchases a $5000 entertainment system by putting a deposit of 10% and financing the rest at 8.6% compounded monthly. If he will make monthly payments for three years, what will the monthly payment be?

I tried 4500 = a(1.0077)^36 but that didn't work and now the problems makes no sense to me.

 

[mmm4444bot]

Here is the formula that I would use to determine the monthly payment amount if $4,500 is borrowed over 36 months at 8.6% APR compounded monthly.

\(\displaystyle A = P\frac{i(1 + i)^n}{(1 + i)^n - 1}\)

A = monthly payment amount

P = principle

i = periodic interest rate

n = total number of payments

Note the word "periodic". This means that symbol i represents the monthly interest rate, not an annual rate. If the 8.6% is stated as APR (which I've assumed that it does for this exercise or your class), then i = 0.086/12.

 

[Denis]

You may be less confused if the formula is stated this way:

P = A * i / (1 + v) where v = 1 / (1 + i)^n

By the way, your .0077 is not correct; .086 / 12 = ?