Final answer:
The present value of an annuity due is described by the statement that the first payment is on the same date as the present value which means the payment occurs immediately at the beginning of the period.
Step-by-step explanation:
When evaluating the present value of an annuity due, it is crucial to understand the timing of the payments as they relate to the calculation of present value. An annuity due is a series of equal payments made at the beginning of each period. Therefore, the correct statement that describes the present value of an annuity due is: B. The first payment is on the same date as the present value. This means that the first payment occurs immediately, and hence, is already at present value, not needing to be discounted back from the future.
Present value calculations help us determine what a future amount of money is worth today, considering a specific interest rate. Take for example a $3,000 bond issued at an 8% interest rate. The initial calculation to find its present value would reveal that the present value is simply the amount currently received or $3,000, demonstrating that the value today for both the borrower and the lender is equivalent. However, should the interest rate increase to 11%, the present value of the future payments would be lower, reflecting the increased cost of borrowing money over time.
To calculate the present value of an annuity due, one would add up all of the present values of the payments, acknowledging the fact that the first payment is already at its present value because it coincides with the valuation date.