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# Present Value Calculator

Single Payment
Periodic Payments
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## 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)

Where:

• 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

Where:

• 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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