PV of Deferred Ordinary Annuity
PV of Deferred Ordinary Annuity
Present value of an annuity that begins after a deferral period of d years.
When to use: Use when payments start after a waiting period, like deferred retirement income.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value today of the deferred annuity | $ |
| PMT | Payment | Periodic payment | $ |
| 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 Pension
A pension pays $40,000/year for 20 years, starting in 10 years. Discount rate 6%.
Given
Step-by-Step
For these inputs, Present Value is $256,189.76 under the stated payment, compounding and accounting assumptions.
Example 2: Deferred Annuity Purchase
Buy an annuity that pays $10,000/year for 15 years starting in 5 years. Rate 5%.
Given
Step-by-Step
For these inputs, Present Value is $81,327.34 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
A deferred annuity is a stream of payments that begins after a waiting period (the deferral period). You might buy one today but not start receiving payments for several years, like a pension that begins at retirement.
The longer the deferral period, the lower the present value. The annuity payments are first valued as if they start immediately, then that value is discounted back by the number of deferral years. Each additional year of deferral reduces the PV.
Common examples include pensions that start at retirement age, deferred compensation plans, structured legal settlements with delayed payments, and insurance products purchased years before the payout phase begins.
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.