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.

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