N I Pv Pmt Fv Calculator

This N I PV PMT FV calculator helps you determine the number of periods (n), interest rate (i), present value (PV), payment (PMT), and future value (FV) in financial calculations. Whether you're analyzing loans, investments, or cash flows, this tool provides quick and accurate results.

What is N I PV PMT FV?

The N I PV PMT FV parameters are fundamental in financial calculations, particularly in time value of money concepts. These parameters help determine the relationship between different financial quantities over time.

In financial mathematics, the time value of money principle states that money available today is worth more than the same amount in the future because it can be invested and earn interest. Conversely, money required in the future is worth less than the same amount today because it would need to be discounted back to account for the interest it could earn.

Key terms:

n - Number of periods (e.g., months, years)
i - Interest rate per period
PV - Present value (current worth)
PMT - Periodic payment (regular payment)
FV - Future value (value at the end of the periods)

How to Use This Calculator

Using this calculator is straightforward. Follow these steps:

Enter the known values for any four of the five parameters (n, i, PV, PMT, FV).
Leave the fifth parameter blank to calculate it.
Click the "Calculate" button to compute the unknown value.
Review the results and chart visualization if available.

The calculator will solve for the missing parameter using the appropriate financial formula. You can also reset the form to start over.

Formulas

The calculator uses the following financial formulas based on the parameters you provide:

Future Value (FV)

FV = PV × (1 + i)ⁿ + PMT × [(1 + i)ⁿ - 1] / i

Present Value (PV)

PV = (FV - PMT × [(1 + i)ⁿ - 1] / i) / (1 + i)ⁿ

Periodic Payment (PMT)

PMT = [FV - PV × (1 + i)ⁿ] × i / [(1 + i)ⁿ - 1]

Number of Periods (n)

n = log[(FV × i + PMT) / (PV × i + PMT)] / log(1 + i)

Interest Rate (i)

This requires numerical methods or iterative solutions and is not directly solvable with a simple formula.

The calculator automatically selects the appropriate formula based on which parameters you provide.

Examples

Let's look at a practical example to see how the calculator works.

Example 1: Calculating Future Value

Suppose you have:

Present Value (PV) = $10,000
Periodic Payment (PMT) = $500
Interest Rate (i) = 5% (0.05)
Number of Periods (n) = 10

Using the Future Value formula:

FV = 10,000 × (1 + 0.05)¹⁰ + 500 × [(1 + 0.05)¹⁰ - 1] / 0.05

FV ≈ $18,787.50

Example 2: Calculating Present Value

Suppose you have:

Future Value (FV) = $20,000
Periodic Payment (PMT) = $1,000
Interest Rate (i) = 6% (0.06)
Number of Periods (n) = 5

Using the Present Value formula:

PV = (20,000 - 1,000 × [(1 + 0.06)⁵ - 1] / 0.06) / (1 + 0.06)⁵

PV ≈ $12,245.50

FAQ

What is the difference between PV and FV?

Present Value (PV) is the current worth of a future sum of money, while Future Value (FV) is the value of a current asset at a future date. PV represents the current cost, and FV represents the future benefit.

How do I know which formula to use?

The calculator automatically selects the appropriate formula based on which parameters you provide. You only need to enter four known values and leave the fifth one blank.

What if I don't know the interest rate?

If you don't know the interest rate, you'll need to estimate it or use additional information to determine it. The calculator cannot solve for the interest rate directly with a simple formula.

Can I use this calculator for loans?

Yes, this calculator can be used for loan calculations where you know the loan amount (PV), monthly payment (PMT), interest rate (i), and loan term (n).

Is this calculator accurate for compound interest?

Yes, the calculator uses compound interest formulas, which account for the interest on both the initial principal and the accumulated interest of previous periods.