Final answer:
The student is being asked to calculate the present value of an annuity due. An annuity due involves payments at the beginning of each period and calculating its present value requires discounting these future payments to present terms and summing them. The exact question involves determining the current worth of a series of payments from a $375,000 retirement fund over 25 years, with a 7.5% interest rate.
Step-by-step explanation:
The student is being asked to determine the present value of an annuity due. An annuity due is a series of equal payments made at the beginning of consecutive periods over a fixed length of time. Here, we're given a future sum ($375,000) that will be received as an annuity due, an interest rate (7.5%), and a time span (25 years). The question is asking what this series of payments is worth in today's dollars. To find the present value of an annuity due, we can use the formula for the present value of an ordinary annuity and adjust it for the fact that payments are made at the beginning of each period. In essence, calculating this requires discounting each individual payment from the future to its value in present terms and then summing those values.
For example, a simple two-year bond issued for $3,000 with an 8% interest rate would pay $240 in interest each year. To find its present value at a discount rate of 8%, we discount the payments received in the first and second year back to the present. If the discount rate changes to 11%, the present value would decrease because the payments are being discounted at a higher rate.
Present Value Calculation
The formula to calculate the present value of each future payment is:
Present Value = Future Payment / (1 + Interest Rate)^Number of Periods
Once all present values are calculated for each period, they are added together to get the total present value of the annuity due.