What is the present value of an annuity that consists of 28 monthly payments of $260 at an interest rate of 8% per year, compounded monthly? (Round your answer to the nearest cent).
To determine the present value of an annuity, you can use the formula for the present value of a series of future cash flows.
The formula for the present value of an annuity is given by:
PV = PMT × (1 - (1 + r/n)^(-nt)) / (r/n)
Where:
PV = Present Value
PMT = Payment amount per period
r = Interest rate per period (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case, the payment amount per period is $260, the interest rate is 8%, compounded monthly (so n = 12), and the number of periods is 28 months (so t = 28/12 = 2.33 years).
Plugging these values into the formula:
PV = $260 × (1 - (1 + 0.08/12)^(-12 × 2.33)) / (0.08/12)
Now we can solve this equation:
PV = $260 × (1 - (1 + 0.0067)^(-28)) / 0.0067
Calculating this expression:
PV = $260 × (1 - 0.6613) / 0.0067
PV = $260 × 0.3387 / 0.0067
PV = $130.74
Therefore, the present value of the annuity is approximately $130.74.