Payment from PV
Calculates the periodic payment for a loan with m-period compounding.
When to use: Use to calculate monthly mortgage or car loan payments.
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 |
| m | Compounding Frequency | Compounding periods per year | integer |
Real-Life Examples
Example 1: Monthly Mortgage Payment
A $350,000 mortgage at 6.5% compounded monthly for 30 years.
Given
Step-by-Step
Monthly mortgage payments are $2,212.24.
Example 2: Auto Loan Payment
Borrow $28,000 for a car at 4.5% monthly compounding for 5 years.
Given
Step-by-Step
Monthly car payments are $521.74.
Frequently Asked Questions
Enter the loan amount as PV, the annual interest rate as k, the loan term in years as n, and 12 for m (monthly payments). The formula gives the fixed monthly payment for a fully amortizing mortgage.
Three factors determine your payment: the loan amount (higher principal means higher payments), the interest rate (higher rates mean higher payments), and the loan term (longer terms lower the payment but increase total interest paid).
Multiply the periodic payment by the total number of payments (n × m), then subtract the original loan amount. The difference is total interest paid. For a 30-year mortgage, total interest often exceeds the original loan amount.