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Annuity-due values at a common date

Both patterns have N payments and are compared at the same specified valuation date.

Read the formula and variables

PVdue=PVord(1+r),FVdue,N=FVord,N(1+r)PV_{due}=PV_{ord}(1+r),\qquad FV_{due,N}=FV_{ord,N}(1+r)

Both patterns have N payments and are compared at the same specified valuation date.

Variables and conventions
InputMeaning
OrdinaryPayments at 1 through N
DuePayments at 0 through N − 1
rRate per payment period

Check a stated example

At 6%, multiplying ordinary PV 4,212.3638 by 1.06 gives due PV 4,465.1056 before rounding.

The amounts in the example are synthetic. Keep the original precision through the calculation and round only the displayed result.

Check the domain and timing

At a negative rate the multiplier is below one. “Due is always higher” needs the positive-rate qualification.

A changed date, payment pattern or quotation convention can require a different expression even when the numbers look similar. Identify those features before calculating.

Further references