Why is the present value of an annuity due greater than that of an ordinary annuity?

The present value of an annuity due is greater than that of an ordinary annuity primarily because the payments of an annuity due occur at the beginning of each period rather than at the end. This timing means that each payment in an annuity due is available to earn interest for an additional period compared to payments made in an ordinary annuity.

When you receive a payment earlier, you have the opportunity to invest that payment immediately, allowing it to start compounding sooner. This compounding effect increases the overall present value of the cash flows from the annuity due. Consequently, since each payment is discounted by a shorter time frame, the present value of these payments when aggregated results in a higher figure compared to the present value of an ordinary annuity, where payments are made at the end of each period.