Payment from PV
Calculates the periodic payment needed to pay off a present value over n periods.
When to use: Use to find loan payments or required withdrawals from a fund.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PMT | Payment | Periodic payment amount | $ |
| PV | Present Value | Current lump sum value | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Time period in years | years |
Real-Life Examples
Example 1: Annual Loan Payment
A $200,000 loan at 5% annual interest over 15 years. What is the annual payment?
Given
Step-by-Step
Annual payments of $19,264.68 will pay off the $200,000 loan in 15 years.
Example 2: Retirement Withdrawals
You have $500,000 and want annual withdrawals over 25 years at 4%.
Given
Step-by-Step
You can withdraw $32,008.70 per year for 25 years.
Frequently Asked Questions
Use this formula with the loan amount as PV, the annual interest rate as k, and the loan term in years as n. The result is the fixed annual payment needed to fully repay the loan over the specified term.
An amortizing loan is one where each payment includes both interest and principal, and the loan is fully repaid by the end of the term. Early payments are mostly interest, while later payments are mostly principal.
Because interest is calculated on the outstanding balance. Early on, the balance is large, so most of the payment covers interest. As the balance decreases with each payment, less goes to interest and more goes to reducing the principal.
Yes. If you know how much you have saved (PV), the expected return (k), and how many years you need income (n), this formula tells you the maximum fixed annual withdrawal that will deplete the fund exactly at the end.