Calculators

Financial

Time Value of Money

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

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.

Number of Years

Use whole numbers or decimals for partial periods such as months, so for 7 years and 6 months you would input 7.5 years

Interest Rate (I)

• The nominal interest rate or stated rate as a percentage

• i = I/100 is the interest rate as a decimal

Compounding

Select daily, monthly or yearly compounding

Future Value (FV)

Future value of a sum of money

Present Value (PV)

The result of the PV calculation is the present value of any future value sum

PVIF

• The Present Value Interest Factor includes time period, interest rate and compounding frequency. You can apply this factor to other future value amounts to find the present value with the same length of investment, interest and compounding rate.

• PVIF = 1 / (1+i)ⁿ

• Multiply any FV by PVIF to get a present value using the same length of investment at the same interest rate.

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%.

1. 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
2. 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
3. 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

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.