Why? Because you can invest and grow cash on hand -- which you cannot do with cash promised. Present value formulas account for this by using an interest rate to discount those future payments.
The present value of the ordinary annuity formula considers the dollar amount of each payment, the discount rate, and the number of payments. The present value of the annuity due formula uses the same inputs but adjusts for the earlier payment timing.
Mathematically, that adjustment involves multiplying the result by the discount rate plus 1. You can see this by comparing the two present value formulas below. Note that "pmt" equals the payment amount, "r" equals the discount rate, and "n" is the total number of payments.
- Present value of ordinary annuity =
pmt [(1–[1/(1+r)^n])/r] - Present value of annuity due =
pmt [(1–[1/(1+r)^n])/r] x (1+r)
The takeaway is that an annuity due will have a higher present value than an ordinary annuity if all other factors are the same.
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