PV of Deferred Annuity Due
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.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value today | $ |
| PMT | Payment | Periodic payment at start of period | $ |
| k | Interest Rate | Discount rate | % |
| n | Number of Years | Payment period length | years |
| d | Deferral Period | Years before payments begin | years |
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
Step-by-Step
For these inputs, Present Value is $46,258.97 under the stated payment, compounding and accounting assumptions.
Example 2: Delayed Insurance Annuity
$25,000/year at start of year for 10 years, beginning in 7 years. Rate 5%.
Given
Step-by-Step
For these inputs, Present Value is $144,051.94 under the stated payment, compounding and accounting assumptions.
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.
The calculator uses the finite zero-rate limit: an annuity’s value is payment times payment count; a solved payment is the target value divided by a positive payment count. Deferral has no effect at zero interest. Values require whole payment counts, even under continuous interest compounding.