Final answer:
The present value of the annuity that pays $250 at the end of each 4 year period for 40 years, given an interest rate of 13.62% and a present value interest factor of an annuity of 4.6986, is $11,746.50.
Step-by-step explanation:
The student is asking about the present value of an annuity with certain terms. To find the present value, we would typically use the formula for the present value of an annuity paid at the end of certain periods. However, since we are given the interest rate (i = 13.62%) and the present value interest factor of an annuity (a = 4.6986), we can simplify the calculation. The formula to calculate the present value (PV) of an annuity is as follows:
PV = R × a
Where R is the payment per period, and a is the present value interest factor of an annuity. In this instance, R = $250 and a = 4.6986.
So, the present value of this annuity is PV = $250 × 4.6986, which results in a PV of $1,174.65. However, since the annuity pays every 4 years for 40 years, we must consider that these payments occur 10 times (40 years divided by 4). So, we multiply our single-period PV by 10:
PV for all periods = $1,174.65 × 10 = $11,746.50.
This is the present value of the annuity. Note that this calculation assumes that the rate and the payment do not change over the period, and that the payments are at the end of each 4-year period.