Personal Finance Calculators

Present Value Calculator

Single Payment
Periodic Payments

The Difference Between the Two Calculators

Both of these present value calculators assess the current worth of future financial amounts, but they apply to different scenarios. The ‘Present Value of a Single Payment’ calculator evaluates the present worth of a lump sum received in the future. In contrast, the ‘Present Value of Periodic Payments’ calculator determines the current value of a series of future payments, akin to an annuity.

Present Value Formula for a Single Payment

The present value formula for a future single payment is:

PV = FV / ((1 + r) ^ t)


  • PV is the present value.
  • FV is the future sum of money.
  • r is the discount rate or interest rate.
  • t represents the number of periods until the money is received.

Let’s use an example to illustrate how to apply the present value formula. Imagine you have the opportunity to receive $10,000 five years from now. You want to figure out how much that $10,000 is worth today. Assume the average annual interest rate in a savings account is 3%.

In this scenario:

  • Future Value (FV): $10,000
  • Discount Rate (r): 3% or 0.03 (as a decimal)
  • Number of Periods (t): 5 years

Using these numbers in the formula, we calculate PV = $8,626.09.

The present value of $10,000, to be received five years from now at a 3% discount rate, is approximately $8,626.09 today. Another way to understand this is: if you had $8,626.09 today and invested it at a 3% annual return, it would grow to $10,000 in five years.

Present Value Formula for Periodic Payments

The present value of periodic payments formula we use in our present value calculator is:

PV = Pmt * (1 – (1 + r) ^ -t) / r


  • PV is the present value of an annuity.
  • Pmt is the fixed amount of each periodic payment.
  • r is the discount rate or interest rate per period.
  • t is the total number of payment periods.

This formula is essentially the present value formula for an annuity. An annuity is a financial product that provides a fixed stream of payments, essentially constituting a series of periodic payments.

To fully grasp this formula, let’s consider an example. Suppose you’re evaluating an investment in an annuity that promises to pay you $5,000 annually for the next 10 years. To determine if it’s a sound investment, you need to calculate the current value of this annuity. Let’s assume the annual discount rate is 4%.

The variables in this scenario are:

  • Periodic Payment (Pmt): $5,000 per year
  • Discount Rate (r): 4% or 0.04 (as a decimal)
  • Total Number of Payment Periods (t): 10 years

By inputting these variables into the formula, we calculate PV = $40,554.48.

The present value of receiving $5,000 annually for 10 years, at a 4% discount rate, is approximately $40,554.48. This means that if you invest $40,554.48 today at a 4% annual return, it would generate an equivalent series of payments totaling $5,000 each year for 10 years.

This example illustrates how to assess the worth of future periodic payment streams in today’s monetary terms, assisting in making informed financial decisions.

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