Question

Charlie cannot remember how much he financed to buy his car. He does remember that his monthly payment is $200. His add-on interest rate was 9% and he made a total of 30 payments. Find the amount of his loan to the nearest penny.

Answer 1

First find the total payments
Total paid
200×30=6,000 (this is the future value)

Second use the formula of the future value of annuity ordinary to find the monthly payment.
The formula is
Fv=pmt [(1+r/k)^(n)-1)÷(r/k)]
We need to solve for pmt
PMT=Fv÷[(1+r/k)^(n)-1)÷(r/k)]
PMT monthly payment?
Fv future value 6000
R interest rate 0.09
K compounded monthly 12
N=kt=12×(30months/12months)=30
PMT=6000÷(((1+0.09÷12)^(30)
−1)÷(0.09÷12))
=179.09 (this is the monthly payment)

Now use the formula of the present value of annuity ordinary to find the amount of his loan.
The formula is
Pv=pmt [(1-(1+r/k)^(-n))÷(r/k)]
Pv present value or the amount of his loan?
PMT monthly payment 179.09
R interest rate 0.09
N 30
K compounded monthly 12
Pv=179.09×((1−(1+0.09÷12)^(
−30))÷(0.09÷12))
=4,795.15

The answer is 4795.15