Final answer:
The present value of an ordinary annuity with quarterly payments of $250 for 7 years at a 12% annual interest rate compounded quarterly is calculated using the annuity present value formula. The question involves converting the annual rate to a quarterly rate and then using this rate along with the number of periods to find the present value, which should match one of the given answer choices.
Step-by-step explanation:
The question is asking to determine the present value of an ordinary annuity that makes regular payments. In this case, it pays $250 every quarter for 7 years, with an interest rate of 12% compounded quarterly. We use the present value formula for an ordinary annuity:
PV = Pmt * [(1 - (1 + r)^{-n}) / r]
Where PV is the present value, Pmt is the payment per period, r is the interest rate per period, and n is the total number of payments.
First, we convert the annual interest rate to a quarterly rate by dividing by 4, since there are 4 quarters in a year:
12% annually is 3% quarterly (0.12 / 4 = 0.03 or 3%). Next, the total number of payments over 7 years given quarterly payments is 28 (7 years * 4 quarters).
Now we substitute these values into the formula to calculate the present value:
PV = $250 * [(1 - (1 + 0.03)^{-28}) / 0.03]
Calculating the above expression will give us the present value of the annuity. Based on the options given in the question, the correct answer to the question is the value that matches one of those options once calculations are complete.