Skip to content

PV of Deferred Annuity Due

Present value of a deferred annuity with payments at the beginning of each period.

When to use: Use when deferred payments are made at the start of each period.

Calculator

Formula

PV=PMT×1(1+k)nk×(1+k)×(1+k)dPV = PMT \times \frac{1 - (1+k)^{-n}}{k} \times (1+k) \times (1+k)^{-d}

Variables

SymbolNameDescriptionUnit
PVPresent ValueValue today$
PMTPaymentPeriodic payment at start of period$
kInterest RateDiscount rate%
nNumber of YearsPayment period lengthyears
dDeferral PeriodYears before payments beginyears

Real-Life Examples

Example 1: Deferred Scholarship

A scholarship pays $15,000/year at start of year for 4 years, beginning in 3 years. Rate 6%.

Given

PMT = 15,000k = 0.06n = 4d = 3

Step-by-Step

1.PVA Due = $15,000 × [1-(1.06)^(-4)]/0.06 × 1.06 = $55,063.94
2.PV = $55,063.94 × (1.06)^(-3)
3.PV = $55,063.94 × 0.83962
4.PV = $46,237.52
Result:46,258.97

The deferred scholarship is worth $46,237.52 today.

Example 2: Delayed Insurance Annuity

$25,000/year at start of year for 10 years, beginning in 7 years. Rate 5%.

Given

PMT = 25,000k = 0.05n = 10d = 7

Step-by-Step

1.PVA Due = $25,000 × [1-(1.05)^(-10)]/0.05 × 1.05 = $202,704.96
2.PV = $202,704.96 × (1.05)^(-7)
3.PV = $202,704.96 × 0.71068
4.PV = $144,052.28
Result:144,052.28

The deferred annuity due is worth $144,052.28 today.

Frequently Asked Questions

A deferred annuity due combines two features: payments begin after a waiting period (deferral), and once they start, they are made at the beginning of each period rather than the end. This provides slightly more value than a deferred ordinary annuity.

First, calculate the present value of the annuity due as if payments started today (using the annuity due formula). Then discount that value back to today by the number of deferral years using the single-sum present value factor.

A deferred annuity due might be used by someone planning for retirement who wants payments at the start of each month or year once retired. The beginning-of-period payments provide income right when each period starts.