PMT Calculator (Periodic Payment)
This PMT Calculator helps you determine the periodic payment (PMT) required for a loan or an investment with a constant interest rate and periodic payments. Input the present value, future value, rate, and periods to find the PMT.
Calculate PMT
What is PMT (Periodic Payment)?
In finance, PMT refers to the periodic payment required to repay a loan (like a mortgage or auto loan) or achieve a future value savings goal over a specified period, with a constant interest rate and regular payments. The PMT Calculator helps determine this fixed payment amount. It’s a fundamental concept in time value of money calculations and is widely used in financial planning, loan amortization, and investment analysis.
The PMT calculation takes into account the present value (e.g., loan amount or initial investment), the future value (target amount, often 0 for loans), the interest rate per period, and the total number of periods. Our PMT Calculator makes finding this value straightforward.
Who should use a PMT Calculator?
- Individuals planning to take out a loan (mortgage, auto, personal) to understand their periodic payment obligations.
- Investors or savers aiming for a specific future value, to determine the regular contributions needed.
- Financial planners and advisors to assist clients with loan and investment planning.
- Students learning about finance and time value of money concepts.
Common Misconceptions
A common misconception is that the PMT only includes principal repayment. In reality, each payment typically consists of both principal and interest (for loans) or principal contribution and interest earned (for investments). The proportion of principal to interest changes over the life of the loan or investment. Another is that the rate used is the annual rate directly; however, the PMT formula uses the rate per period (annual rate divided by periods per year).
PMT Formula and Mathematical Explanation
The PMT is calculated using the following formulas, depending on whether payments are made at the end or beginning of each period:
Let:
- PV = Present Value
- FV = Future Value
- r = Interest rate per period (Annual Rate / Periods per Year)
- n = Total number of periods (Years * Periods per Year)
If payments are made at the end of each period (Ordinary Annuity):
PMT = [r * (FV + PV * (1 + r)^n)] / [(1 + r)^n - 1]
If FV is 0 (like a standard loan payoff), this simplifies to:
PMT = [PV * r * (1 + r)^n] / [(1 + r)^n - 1]
If PV is 0 (like a savings goal from scratch), this simplifies to:
PMT = [FV * r] / [(1 + r)^n - 1]
If payments are made at the beginning of each period (Annuity Due):
PMT = [r * (FV + PV * (1 + r)^n)] / [((1 + r)^n - 1) * (1 + r)]
Our PMT Calculator uses these formulas based on your input.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| PV | Present Value | Currency (e.g., $) | 0 or positive value |
| FV | Future Value | Currency (e.g., $) | 0 or positive value |
| Annual Rate | Annual interest/growth rate | % | 0 – 30% (can vary) |
| Years | Total number of years | Years | 1 – 50 (can vary) |
| Periods per Year | Number of payments per year | Number | 1, 2, 4, 12 |
| r | Rate per period | Decimal | (Annual Rate / 100) / Periods per Year |
| n | Total number of periods | Number | Years * Periods per Year |
| PMT | Periodic Payment | Currency (e.g., $) | Calculated value |
Practical Examples (Real-World Use Cases)
Example 1: Loan Repayment
Someone wants to borrow $50,000 (PV) for a car. The annual interest rate is 6%, the loan term is 5 years, and payments are monthly. FV is $0 as the loan will be paid off. Payments are at the end of the period.
- PV = 50000
- FV = 0
- Annual Rate = 6%
- Years = 5
- Periods per Year = 12
- Payment Timing = End
Using the PMT Calculator with these inputs, the monthly payment (PMT) would be approximately $966.64. Over 5 years, they would pay a total of $57,998.40, with $7,998.40 being interest.
Example 2: Savings Goal
Someone wants to save $100,000 (FV) over 10 years by making monthly contributions to an investment account earning an estimated 4% annually. They start with $0 (PV). Payments are at the end of the period.
- PV = 0
- FV = 100000
- Annual Rate = 4%
- Years = 10
- Periods per Year = 12
- Payment Timing = End
The PMT Calculator would show they need to contribute approximately $679.34 per month to reach their goal of $100,000 in 10 years, assuming a 4% annual return.
How to Use This PMT Calculator
- Enter Present Value (PV): Input the initial amount. For a loan, this is the loan amount. For savings, it could be your starting balance (or 0).
- Enter Future Value (FV): Input the target amount at the end. For a loan, this is usually 0. For savings, this is your goal.
- Enter Annual Rate (%): Input the annual interest rate or expected rate of return.
- Enter Period (Years): Input the total duration in years.
- Select Periods per Year: Choose how often payments are made (e.g., monthly).
- Select Payment Timing: Choose if payments occur at the start or end of each period.
- Click “Calculate PMT”: The calculator will display the periodic payment (PMT), total principal, total interest/earnings, and total cost/value.
How to Read Results
The primary result is the “Periodic Payment (PMT)”. Intermediate results show the total amount paid/contributed, total principal, and total interest/earnings over the entire term. The chart visually shows the balance changing over time. Our Amortization Schedule Calculator can give a more detailed breakdown.
Key Factors That Affect PMT Results
- Present Value (PV): A higher PV (e.g., larger loan amount) will result in a higher PMT, all else being equal.
- Future Value (FV): If aiming for a higher FV (savings goal), the PMT will be higher. If FV is 0 for a loan, it’s factored differently than a non-zero FV.
- Annual Rate: A higher annual rate increases the interest component, leading to a higher PMT for loans, or requiring a lower PMT for savings to reach a goal if the rate is higher (more earnings). Our Interest Rate Calculator explores rate impacts.
- Period (Years) & Periods per Year: A longer term (more years or more periods) generally reduces the PMT for loans but increases total interest paid. For savings, a longer term might reduce the required PMT for a fixed goal.
- Payment Timing: Payments made at the beginning of the period (Annuity Due) usually result in a slightly lower PMT compared to end-of-period payments (Ordinary Annuity) because the money is working for you (or against you for a loan) for one extra period.
- Compounding Frequency: Although the calculator asks for Periods per Year for payments, the rate per period (r) is derived from this, implicitly linking to compounding frequency if it matches payment frequency. More frequent compounding (and payments) can affect the total amount.
Frequently Asked Questions (FAQ)
PMT stands for Periodic Payment. It’s the regular, fixed amount paid or received in an annuity or loan repayment schedule.
Yes, you can use this PMT Calculator for mortgage payments. Enter the loan amount as PV, 0 as FV, the annual interest rate, the loan term in years, and select 12 periods per year (for monthly payments). You might also find our Mortgage Payment Calculator useful.
This PMT Calculator assumes a constant interest rate over the entire term. If the rate changes (e.g., variable-rate loan), the PMT will also change, and this calculator won’t reflect that dynamic change accurately over the full term without re-calculation at each rate change.
Payments at the start of the period (annuity due) mean each payment has one more period to earn interest (or reduce principal earlier). This generally results in a slightly lower PMT compared to payments at the end (ordinary annuity) for the same PV, FV, rate, and term.
Yes. Set PV to your current savings (or 0), FV to your savings goal, enter the expected annual rate of return, the number of years, and periods per year. The PMT Calculator will show the regular contribution needed.
This PMT Calculator focuses on finding the single periodic payment amount. A Loan Amortization Calculator typically provides the PMT and also a detailed schedule showing how each payment is split between principal and interest over the entire loan term.
Minor differences can occur due to rounding methods, or if the bank includes other fees or uses a slightly different day-count convention for interest calculation. This PMT Calculator uses standard financial formulas.
This calculator calculates the fixed PMT without considering extra payments. Making extra payments on a loan would reduce the principal faster and shorten the loan term, reducing total interest paid. Our Loan Payment Calculator might offer more options for extra payments.