Loan amount = $10,000
Monthly payments = $258.50
Time of loan contract = 5 years
True annual interest rate?
To calculate the true annual interest rate, we need to use the loan amount, monthly payments, and the time of the loan contract. In this case, we have:
Loan amount = $10,000
Monthly payments = $258.50
Time of loan contract = 5 years
To calculate the true annual interest rate, we can use the present value formula for an ordinary annuity. The formula is:
PV = P * [1 - (1 + r)^(-n)] / r
Where:
PV = Present value or loan amount ($10,000)
P = Monthly payment ($258.50)
r = True annual interest rate (what we want to find)
n = Number of compounding periods (in this case, 5 years with monthly payments, so n = 5 * 12 = 60)
Rearranging the formula to solve for r:
r = [1 - (PV / P)]^(-1/n) - 1
Substituting the values into the formula:
r = [1 - (10,000 / 258.50)]^(-1/60) - 1
Calculating this expression will give us the true annual interest rate.