Finance calculators

TVM Calculator

Updated Jun 20, 2026 By Jehan Wadia
Formulas

TVM Inputs & Controls

Enter four known values, then press a Solve button (or the main Calculate button) to compute the fifth. Use negative numbers for cash outflows (money you pay out).

Total number of payment periods.
Annual interest rate.
Present value; negative for outflow.
Payment each period; negative for outflow.
Future value; negative for outflow.
Governs how often interest compounds and payments occur.

Results Summary

Payment (PMT)
$0.00
Total of All Payments
$0.00
Total Interest
$0.00
Inputs Used

Step-by-Step Solution

Balance & Cumulative Interest

Amortization Schedule

Period Opening Balance (PV) Payment (PMT) Interest Closing Balance (FV)

Introduction

The Time Value of Money (TVM) Calculator helps you figure out how money grows or shrinks over time. A dollar today is worth more than a dollar in the future because you can invest it and earn interest. This simple idea is the foundation of all finance.

With this calculator, you can solve for any one of five key variables: the number of periods (N), the interest rate (I/Y), the present value (PV), the payment amount (PMT), or the future value (FV). Just enter the four values you know, and the calculator finds the fifth. It works for loans, mortgages, savings plans, retirement goals, and any other situation where money earns or costs interest over time.

You also get a full amortization schedule, a step-by-step solution showing the math, and an interactive chart that plots your balance and total interest paid across every period. Advanced settings let you change compounding frequency, choose between nominal and effective rates, and switch between ordinary annuity and annuity due timing.

How to Use Our TVM Calculator

This Time Value of Money calculator solves for one unknown value when you enter the other four. Fill in four of the five fields below, then press the matching Solve button to find the missing value.

N — Periods: Enter the total number of payment periods. For example, a 30-year mortgage paid monthly has 360 periods.

I/Y — Interest Rate: Enter the annual interest rate as a percent. For example, type 6.5 for a 6.5% rate.

PV — Present Value: Enter the current value of the loan or investment. Use a negative number if this is money you pay out, such as an initial investment. You can also use our standalone Present Value Calculator for quick PV-only problems.

PMT — Payment: Enter the amount paid or received each period. Use a negative number for payments you make, like monthly loan payments.

FV — Future Value: Enter the value at the end of all periods. For a loan paid in full, this is 0. For a savings goal, enter your target amount. Our dedicated Future Value Calculator can also handle this quickly.

Compounding / Payment Frequency: Choose how often payments are made and interest compounds. Common choices are monthly, quarterly, or annually.

Advanced Settings: Click this button if you need to set compounding and payment frequencies separately, switch between nominal (APR) and effective (EAR) rates, or change payment timing from end of period to beginning of period.

After you press Calculate, the calculator shows your result, total payments, total interest, a step-by-step solution, a balance chart, and a full amortization schedule.

What Is the Time Value of Money?

The time value of money (TVM) is a simple idea: a dollar today is worth more than a dollar in the future. Why? Because you can invest that dollar today and earn interest on it. Over time, your money grows. This growth is called compounding. You can explore this concept further with our Compound Interest Calculator.

Think of it this way. If someone offered you $100 right now or $100 a year from now, you should take it now. You could put that $100 in a savings account, earn interest, and have more than $100 by next year. The money you have right now has more value because it has more time to grow.

The Five TVM Variables

Every time value of money problem uses five key variables. If you know four of them, you can solve for the fifth.

  • N (Number of Periods): The total number of times a payment is made or interest is applied. For a 30-year mortgage paid monthly, N equals 360.
  • I/Y (Interest Rate per Year): The annual interest rate on the loan or investment.
  • PV (Present Value): The amount of money you have or owe right now. For a loan, this is the amount you borrow. For an investment, this is what you put in today.
  • PMT (Payment): The amount paid or received each period. Monthly mortgage payments and regular savings deposits are common examples.
  • FV (Future Value): The amount of money you will have or owe at the end of all the periods. For a fully paid-off loan, FV is zero. For a savings goal, FV is your target amount.

How the Cash Flow Sign Convention Works

In TVM calculations, money flowing in different directions uses different signs. Money you pay out (like a loan payment or an initial investment) is entered as a negative number. Money you receive (like a loan deposit into your account or a future payout) is entered as a positive number. Getting the signs right is important. If your answer looks wrong, check your signs first.

Common Uses for a TVM Calculator

People use time value of money calculations every day for real financial decisions:

  • Mortgage payments: Find out how much your monthly payment will be on a home loan.
  • Car loans: Calculate the payment on an auto loan or figure out how much car you can afford.
  • Savings goals: Determine how much to save each month to reach a future goal like college tuition or retirement.
  • Investment growth: See how much a lump sum invested today will be worth in the future. A quick estimate uses the Rule of 72 to find how long it takes money to double.
  • Loan comparisons: Compare different interest rates or loan terms to find the best deal.

Payment Timing: End vs. Beginning of Period

Payments can happen at the end or the beginning of each period. Most loans use end-of-period payments, called an ordinary annuity. Some leases and rent payments happen at the start of the period, called an annuity due. Our Annuity Calculator is a great companion tool for exploring these scenarios. This small difference changes the result because money paid earlier has more time to earn or cost interest.

Compounding Frequency

Compounding frequency tells you how often interest is calculated and added to the balance. The more often interest compounds, the faster money grows. Monthly compounding adds interest 12 times a year. Daily compounding adds it 365 times a year. A nominal rate (APR) is the stated annual rate before compounding. An effective rate (EAR) is the true annual rate after compounding is factored in. You can use our APY Calculator to quickly convert between nominal and effective rates. For situations involving only a single lump sum with no recurring payments, our Simple Interest Calculator can provide a useful comparison against compound growth.


Formulas used

Core TVM Equation
PV \cdot (1+i)^{N} + PMT \cdot (1+i \cdot t) \cdot \frac{(1+i)^{N}-1}{i} + FV = 0
Solve for Future Value (FV)
FV = -\left[PV \cdot (1+i)^{N} + PMT \cdot (1+i \cdot t) \cdot \frac{(1+i)^{N}-1}{i}\right]
Solve for Present Value (PV)
PV = \frac{-\left[PMT \cdot (1+i \cdot t) \cdot \frac{(1+i)^{N}-1}{i} + FV\right]}{(1+i)^{N}}
Solve for Payment (PMT)
PMT = \frac{-\left[PV \cdot (1+i)^{N} + FV\right]}{(1+i \cdot t) \cdot \frac{(1+i)^{N}-1}{i}}
Solve for Number of Periods (N)
N = \frac{\ln\!\left(\frac{PMT(1+i \cdot t)/i - FV}{PV + PMT(1+i \cdot t)/i}\right)}{\ln(1+i)}
Periodic Rate from Nominal (APR)
i = \left(1 + \frac{r}{C/Y}\right)^{C/Y \,/\, P/Y} - 1

Frequently asked questions

What does negative mean when I enter a number?

A negative number means money you pay out. For example, if you borrow $200,000, that money comes to you, so PV is positive. Your monthly payment leaves your pocket, so PMT is negative. If your answer looks wrong, check your signs first.

Which variable should I solve for?

Enter the four values you already know and leave the fifth blank. Then click the Solve button next to the blank field. For instance, if you know the loan amount, rate, term, and final balance but not the payment, click Solve PMT.

Why does the calculator say no valid solution found?

This usually means the signs on PV, PMT, and FV conflict with each other. In a typical loan, PV is positive (money received), PMT is negative (money paid out), and FV is zero. Make sure at least one value is positive and at least one is negative.

What is the difference between C/Y and P/Y?

C/Y is how many times per year interest compounds. P/Y is how many payments you make per year. Most of the time they are the same. If your bank compounds daily but you pay monthly, you would set C/Y to 365 and P/Y to 12 in the Advanced Settings.

How do I calculate a monthly mortgage payment?

Set N to the total number of months (for example, 360 for 30 years). Enter the annual rate in I/Y. Put the loan amount in PV. Set FV to 0. Choose Monthly frequency. Then click Solve PMT. The result is your monthly payment.

How do I find out how long it takes to pay off a loan?

Enter the loan balance in PV, the annual rate in I/Y, your payment as a negative number in PMT, and 0 in FV. Then click Solve N. The answer is the number of periods needed to pay off the loan.

What is the difference between nominal and effective rate?

A nominal rate (APR) is the stated annual rate before compounding. An effective rate (EAR) is the true annual rate after compounding is included. For example, a 6% nominal rate compounded monthly gives an effective rate of about 6.17%. You can switch between them in Advanced Settings.

Can I use this calculator for savings and investments?

Yes. To find how much a savings plan will grow, enter your starting deposit as a negative PV (money you put in), your regular deposit as a negative PMT, the interest rate in I/Y, and the number of periods in N. Then click Solve FV to see the future value.

What does the amortization schedule show?

The amortization schedule breaks every period into four parts: the opening balance, the payment, the interest charged that period, and the closing balance. It shows exactly how much of each payment goes to interest and how much reduces the balance.

Why is my solved value slightly different from my bank statement?

Small differences can come from rounding. Banks often round each payment to the nearest cent and may adjust the final payment. This calculator uses full precision math, so results may differ by a few cents over many periods.

What happens if the interest rate is 0%?

The calculator handles a 0% rate correctly. With no interest, money does not grow or shrink. Payments simply divide the total amount evenly across all periods. For example, a $12,000 loan over 12 months at 0% gives a $1,000 monthly payment.

How do I figure out what interest rate I am paying?

Enter the loan amount in PV, the payment as a negative number in PMT, the number of periods in N, and the remaining balance in FV (usually 0). Then click Solve I/Y. The calculator finds the annual rate using a numerical method.

What is an annuity due and when should I use it?

An annuity due means payments happen at the start of each period instead of the end. Rent and lease payments often work this way. If your first payment is due right away, switch to Beginning of Period in Advanced Settings.

Can I set compounding and payment frequencies to different values?

Yes. Click Advanced Settings to see separate dropdowns for C/Y (compounding periods per year) and P/Y (payment periods per year). This is useful when, for example, interest compounds daily but payments are made monthly.

What does the chart show?

The chart plots two lines over time. The blue line shows the remaining balance after each period. The green line shows the total interest paid so far. Together they help you see how quickly the balance drops and how much interest builds up.

Is there a limit on the number of periods?

You can enter up to 100,000 periods. However, the amortization schedule table is capped at 10,000 rows for performance. The solved value, totals, and chart still use the full number of periods you entered.

How do I calculate how much I can borrow?

Enter the number of periods in N, the annual rate in I/Y, the payment you can afford as a negative number in PMT, and 0 in FV. Then click Solve PV. The result is the maximum loan amount you can take on with that payment.

What does the step-by-step solution do?

It shows every formula and substitution used to reach the answer. You can see the periodic rate calculation, the annuity factor, and the final algebra. This is helpful for students learning TVM math or anyone who wants to verify the result by hand.