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Comparing ordinary and due annuity values

Five payments of 1,000 at 6% per period have ordinary PV 4,212.3638 and due PV 4,465.1056.

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Place all five payments

The ordinary pattern pays at times 1 to 5. The due pattern pays at times 0 to 4. Both present values are measured at time zero.

Compare the discounted terms

Payments under the two patterns
Payment positionOrdinary dateDue date
First10
Second21
Third32
Fourth43
Fifth54

Apply the one-period shift

Multiplying the unrounded ordinary value by 1.06 gives the due value. The difference is 252.7418. The factor changes every payment’s discount exponent by one.

Keep the future date consistent

At time 5, ordinary FV is 5,637.093 and due FV is 5,975.3185. The due final payment at time 4 has one growth period before that comparison date.

Further references