Calculators

Financial

Time Value of Money

Calculator Use

Calculate the Future Value and Future Value Interest Factor (FVIF) for a present value invested for a future return. Our basic future value calculator sets time periods to years with interest compounded daily, monthly, or yearly.

The Future Value Formula

Where:

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

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

When using this future value formula be sure 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 future value calculations see our other future value calculators. See the Future Value of a Dollar calculator to create a table of FVIF 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

Present Value (PV)

Present value of a sum of money to be invested

Future Value (FV)

The result of the FV calculation is the future value of a present value sum to be invested for some number of years at a given interest rate

FVIF

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

• FVIF = (1+i)ⁿ

• Multiply any PV by FVIF to get a future value with the same length of investment at the same interest rate.

Future Value Example Problem

The default calculation in the calculator asks what is the future value of a present value amount of $12,487.16 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 future value formula FV = PV*(1+i)ⁿ
   \( FV = PV(1+i)^n \)
   \( FV = 12487.16(1+0.004375)^{42} \)
   \( FV = 12487.16(1.004375)^{42} \)
   \( FV = 12487.16(1.201233824) \)
   \( FV = 15000.00 \)

Future Value Interest Factor Example Problem

Calculating the Future Value Interest Factor FVIF for this same problem, FVIF = (1+i)ⁿ

Use this FVIF to find the future value of any present value with the same investment length and interest rate. Instead of a present value of $12487.16, perhaps you want to find the future value of a present value of $16,649.60.