PV of Ordinary Annuity
Calculates the present value of periodic payments with m-period discounting.
When to use: Use for monthly loan payments, leases, or any periodic payment stream.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PVA | Present Value of Annuity | Total present value of all payments | $ |
| PMT | Payment | Periodic payment amount | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Time period in years | years |
| m | Compounding Frequency | Compounding periods per year | integer |
Real-Life Examples
Example 1: Mortgage Valuation
A mortgage requires $1,500/month for 30 years at 6% compounded monthly. What is the loan amount?
Given
Step-by-Step
The mortgage principal supported by $1,500/month payments is $250,187.44.
Example 2: Auto Loan
Car payments of $400/month for 5 years at 5% compounded monthly.
Given
Step-by-Step
You can borrow $21,196.29 for a car at these terms.
Frequently Asked Questions
Divide the annual rate by 12 for the monthly discount rate and multiply years by 12 for total payments. Then use the present value of annuity formula with these adjusted values.
Use this formula with your affordable monthly payment as PMT, the loan interest rate divided by 12 as the periodic rate, and the loan term in months. The result is the maximum loan amount those payments support.
A longer loan term means more total payments, so the stream of cash flows is worth more in present value terms. However, the incremental value of each additional year decreases because distant payments are heavily discounted.