A man agrees to pay $450 per month for 48 months to pay off a car loan. If interest of is charged at 12% compounded monthly, how much did the car originally cost?
12/12 = 1% per month
total paid = 450 * 48 = 21,600
21,600 = x (1.01)^48
x = 13,397.62
To find the original cost of the car, we need to use the formula for the present value of an ordinary annuity.
The formula for the present value of an ordinary annuity is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value (original cost of the car)
PMT = Monthly payment ($450)
r = Monthly interest rate (12% / 12 = 0.01)
n = Number of months (48)
Now, let's plug in the values into the formula and solve for PV:
PV = 450 * (1 - (1 + 0.01)^(-48)) / 0.01
To solve this equation, we need to use a calculator or a spreadsheet program. By substituting the numbers:
PV ≈ $14,851.89
Therefore, the original cost of the car was approximately $14,851.89.