Payment from PV
Calculates the beginning-of-period payment to pay off a present value.
When to use: Use to find lease payments or beginning-of-period withdrawals.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PMT | Payment | Periodic payment amount (paid at start of period) | $ |
| PV | Present Value | Current lump sum value | $ |
| k | Interest Rate | Nominal annual interest rate | % |
| n | Number of Years | Time period in years | years |
Real-Life Examples
Example 1: Annual Lease Payment
Equipment worth $50,000, lease at 8% for 5 years, payments at start of year.
Given
Step-by-Step
Beginning-of-year lease payments are $11,596.85.
Example 2: Retirement Withdrawals
$300,000 nest egg, withdraw at start of each year for 20 years, 5% rate.
Given
Step-by-Step
You can withdraw $22,926.64 at the start of each year.
Frequently Asked Questions
Enter the asset value or lease amount as PV, the annual rate as k, and the lease term as n. The formula gives the annual payment due at the start of each year that will fully amortize the lease.
Because each payment is made one period earlier, it earns interest for one extra period. This extra earning power means smaller payments are needed to achieve the same financial result.
Yes. Enter your retirement savings as PV, expected return as k, and years of retirement as n. The result is the maximum beginning-of-year withdrawal that depletes the fund by the end of the term.