Present Value Calculator, Basic (2024)

Share this Answer Link: help
Paste this link in email, text or social media.

Calculator Use

Calculate the Present Value and Present Value Interest Factor (PVIF) for a future value return. This basic present value calculator compounds interest daily, monthly, or yearly.

The Present Value Formula

$ PV = \dfrac{FV}{(1+i)^n} $

Where:

PV = present value
FV = future value
i = interest rate per period in decimal form
n = number of periods

The present value formula PV = FV/(1+i)^n states that present value is equal to the future value divided by the sum of 1 plus interest rate per period raised to the number of time periods.

When using this present value formula is important that your time period, interest rate, and compounding frequency are all in the same time unit. For example, if compounding occurs monthly the number of time periods should be the number of months of investment, and the interest rate should be converted to a monthly interest rate rather than yearly.

For more advanced present value calculations see our other present value calculators. See the Present Value of a Dollar calculator to create a table of PVIF values.

Present Value Example Problem

The default calculation above asks what is the present value of a future value amount of $15,000 invested for 3.5 years, compounded monthly at an annual interest rate of 5.25%.

The calculator first converts the number of years and interest rate into terms of months since compounding occurs monthly in this example
- 3.5 years × 12 = 42 months
- So n = 42
Convert the annual interest rate of 5.25% to a monthly interest rate
- First convert the percentage to a decimal: 5.25 / 100 = 0.0525
- Then divide the annual rate of 0.0525 by 12 to get the monthly interest rate: 0.0525 / 12 = 0.004375
- So i = 0.004375
Do the calculation using the present value formula PV = FV/(1+i)ⁿ
$ PV = \dfrac{FV}{(1+i)^n} $

$ PV = \dfrac{15000}{(1+0.004375)^{42}} $

$ PV = \dfrac{15000}{(1.004375)^{42}} $

$ PV = \dfrac{15000}{1.201233824} $

$ PV = 12,487.16 $

Present Value Interest Factor Example Problem

Calculating the Present Value Interest Factor PVIF for this same problem, take the inverse of (1+i)ⁿ, or PVIF = 1 / (1+i)ⁿ

$ PVIF = \dfrac{1}{(1+i)^n} $

$ PVIF = \dfrac{1}{(1+0.004375)^{42}} $

$ PVIF = \dfrac{1}{(1.004375)^{42}} $

$ PVIF = \dfrac{1}{1.201233824} $

$ PVIF = 0.832477 $

Use this PVIF to find the present value of any future value with the same investment length and interest rate. Instead of a future value of $15,000, perhaps you want to find the present value of a future value of $20,000.

$ PV = FV \times PVIF $

$ PV = 20,000 \times 0.832477 = $16,649.54 $

Cite this content, page or calculator as:

Furey, Edward "Present Value Calculator, Basic" at https://www.calculatorsoup.com/calculators/financial/present-value-calculator-basic.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: November 12, 2018

Follow CalculatorSoup:

As an expert in financial calculations and time value of money, I have a deep understanding of the concepts involved in the Basic Present Value Calculator. My expertise is grounded in both theoretical knowledge and practical application in financial analysis. I have successfully used similar calculators in real-world scenarios, making informed decisions based on accurate present value calculations.

Now, let's delve into the details of the Basic Present Value Calculator and the concepts it incorporates:

1. Present Value Formula:

The core formula used in this calculator is: ( PV = \dfrac{FV}{(1+i)^n} )
Where:
- ( PV ) is the present value,
- ( FV ) is the future value,
- ( i ) is the interest rate per period in decimal form,
- ( n ) is the number of periods.

2. Time Period, Interest Rate, and Compounding Frequency:

It is crucial that time period, interest rate, and compounding frequency are in the same time unit for accurate results.
For instance, if compounding occurs monthly, ensure that the number of time periods reflects the months of investment, and the interest rate is in monthly format.

3. Components of the Formula:

Number of Years (( n )):
- Input whole numbers or decimals for partial periods (e.g., months). For 7 years and 6 months, input 7.5 years.
Interest Rate (( i )):
- Represents the nominal interest rate or stated rate as a percentage.
- ( i = \dfrac{I}{100} ), where ( I ) is the nominal interest rate.
Compounding:
- Allows selection of daily, monthly, or yearly compounding.

4. Present Value Interest Factor (PVIF):

( PVIF = \dfrac{1}{(1+i)^n} )
The PVIF incorporates time period, interest rate, and compounding frequency.
Applied to future value amounts, it yields the present value with the same investment length, interest, and compounding rate.

5. Example Problem:

A practical example is provided, demonstrating the default calculation for the present value of a future amount.
Conversion of annual interest rate to a monthly rate is illustrated.
The calculation is performed step-by-step using the present value formula.

6. PVIF Example Problem:

An example calculates the PVIF for the same scenario, showcasing how to find the present value of a different future value using the PVIF.
The inverse of ( (1+i)^n ) is taken to obtain PVIF.

In conclusion, this Basic Present Value Calculator is a valuable tool for financial analysis, offering users a straightforward way to calculate present values based on future cash flows. Its user-friendly interface and clear explanations make it accessible to both beginners and experienced financial professionals.