Perpetuity Due
A perpetuity whose payments arrive at the beginning of each period rather than the end, so it is worth exactly one payment more than the ordinary perpetuity.
PV of Perpetuity Due (Annual Compounding)
Present value of infinite payments made at the beginning of each period.
When to use: Use when perpetual payments are made at the start of each period.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value of the perpetuity due | $ |
| PMT | Payment | Periodic payment | $ |
| k | Interest Rate | Discount rate | % |
Real-Life Examples
Example 1: Prepaid Perpetuity
A trust pays $8,000/year at the start of each year forever. Discount rate 4%.
Given
Step-by-Step
For these inputs, Present Value is $208,000.00 under the stated payment, compounding and accounting assumptions.
Example 2: Scholarship Fund
A scholarship of $20,000/year paid at start of year forever. Discount rate 5%.
Given
Step-by-Step
For these inputs, Present Value is $420,000.00 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
A perpetuity due is an infinite stream of equal payments made at the beginning of each period. It is worth more than an ordinary perpetuity because the first payment is received immediately and every subsequent payment arrives one period earlier.
A perpetuity due is worth exactly one extra payment more than the ordinary perpetuity. Its value equals PMT + PMT/k, which is the ordinary perpetuity value (PMT/k) plus the immediate first payment (PMT).
Perpetuities due arise when payments are collected or distributed at the start of each period indefinitely — like a scholarship fund that disburses at the beginning of each academic year, or prepaid perpetual lease arrangements.