# Future Value of a Present Sum Calculator

## Calculator Use

Calculate the future value return for a present value lump sum investment, or a one time investment, based on a constant interest rate per period and compounding. To include an annuity use a comprehensive future value calculation.

- Period
- commonly a period will be a year but it can be any time interval you want as long as all inputs are consistent.
- Investment (PV)
- is the present value or principal amount to be invested.
- Interest Rate (R)
- is the annual nominal interest rate or "stated rate" in percent. r = R/100, the interest rate in decimal
- Number of Periods (t)
- commonly this will be number of years but periods can be any time unit. Enter whole numbers or use decimals for partial periods such as months for example, 7.5 years is 7 yr 6 mo.
- Compounding (m)
- is the number of times compounding occurs per period. If a period is a year then annually=1, quarterly=4, monthly=12, daily = 365, etc.
- Continuous Compounding
- is when the frequency of compounding (m) is increased up to infinity. Enter c, C or Continuous for m.
- Interest Rate (i)
- i = (r/m); interest rate per compounding period.
- Total Number of Periods (n)
- n = mt; is the total number of compounding periods for the life of the investment.
- Future Value (FV)
- the calculated future value of our investment
- FVIF
- Future Value Interest Factor that accounts for your input Number of Periods, Interest Rate and Compounding Frequency and can now be applied to other present value amounts to find the future value under the same conditions.

## Future Value Formula for a Present Value:

where r=R/100 and is generally applied with r as the yearly interest rate, t the number of years and m the number of compounding intervals per year. Although, we can think of r as a rate per period, t the number of periods and m the compounding intervals per period where a period is any interval of time. We can reduce this to the more general

where i=r/m and n=mt with i the rate per compounding period and n the number of compounding periods.

When m approaches infinity, m → ∞ (continuous compounding)

Future Value Formula Derivations

**Example Future Value Calculations for a Lump Sum Investment:**

You put $10,000 into an ivestment account earning 6.25% per year compounded monthly. You want to know the value of your investment in 2 years or, the future value of your account.

- Investment (pv) = $10,000
- Interest Rate (R) = 6.25%
- Number of Periods (years) (t) = 2
- Compounding per Period (per year) (m) = 12