Using the formula, compute the true annual interest rate.
Loan amount = $9,500
Monthly payments = $227.50
Time of loan contract = 5 years
True annual interest rate (to the nearest tenth
What formula?
To compute the true annual interest rate, we can use the formula for calculating the present value of an ordinary annuity:
PV = P * ((1 - (1 + r)^(-n)) / r)
Where:
PV = Present Value (Loan amount)
P = Monthly payment
r = Monthly interest rate
n = Number of payments
In this case, we need to find the monthly interest rate (r) that will allow us to compute the present value (PV) as the given loan amount ($9,500) and the number of payments (n) over the duration of the loan (5 years).
Step 1: Convert the loan time from years to months by multiplying it by 12:
n = 5 years * 12 months/year
n = 60 months
Step 2: Rearrange the formula to solve for r:
PV = P * ((1 - (1 + r)^(-n)) / r)
r = ((1 - (PV / P)) / (PV / P))^(1 / (-n)) - 1
Step 3: Plug in the given values into the formula:
PV = $9,500
P = $227.50
n = 60
r = ((1 - (9500 / 227.50)) / (9500 / 227.50))^(1 / (-60)) - 1
After evaluating this expression, the true annual interest rate (to the nearest tenth) will be the value of r.