# Future Value of Annuity Calculator

## Calculator Use

Use this calculator to find the future value of annuities due, ordinary regular annuities and growing annuities.

- Period
- commonly a period will be a year but it can be any time interval you want as long as all inputs are consistent.
- Number of Periods (t)
- number of periods or years
- Perpetuity
- for a perpetual annuity t approaches infinity. Enter p, P, perpetuity or Perpetuity for t
- Interest Rate (R)
- is the annual nominal interest rate or "stated rate" per period in percent. r = R/100, the interest rate in decimal
- 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, continuous or Continuous for m.
- Payment Amount (PMT)
- The amount of the annuity payment each period
- Growth Rate (G)
- If this is a growing annuity, enter the growth rate per period of payments in percentage here. g = G/100
- Payments per Period (Payment Frequency (q))
- How often will payments be made during each period? If a period is a year then annually=1, quarterly=4, monthly=12, daily = 365, etc.
- Payments at Period (Type)
- Choose if payments occur at the
or if payments occur at the*end of each payment period (ordinary annuity, in arrears, 0)**beginning of each payment period (annuity due, in advance, 1)* - Future Value (FV)
- the future value of any present value cash flows (payments)

## Future Value Annuity Formulas:

You can find derivations of future value formulas with our future value calculator.

### Future Value of an Annuity

\[ FV=\frac{PMT}{i}[(1+i)^n-1](1+iT) \]where r = R/100, n = mt where n is the total number of compounding intervals, t is the time or number of periods, and m is the compounding frequency per period t, i = r/m where i is the rate per compounding interval n and r is the rate per time unit t. If compounding and payment frequencies do not coincide, r is converted to an equivalent rate to coincide with payments then n and i are recalculated in terms of payment frequency, q.

If type is ordinary, T = 0 and the equation reduces to the formula for **future value of an ordinary annuity**

otherwise T = 1 and the equation reduces to the formula for **future value of an annuity due**

### Future Value of a Growing Annuity (g ≠ i)

where g = G/100

\[ FV=\frac{PMT}{(i-g)}\left[(1+i)^{n}-(1+g)^{n}\right](1+iT) \]### Future Value of a Growing Annuity (g = i)

\[ FV=PMTn(1+i)^{n-1}(1+iT) \]**Future Value of a Perpetuity or Growing Perpetuity (t → ∞)**

For g < i, for a perpetuity, perpetual annuity, or growing perpetuity, the number of periods t goes to infinity therefore n goes to infinity and, logically, the future value goes to infinity.

## Continuous Compounding (m → ∞)

Again, you can find these derivations with our future value formulas and our future value calculator.

### Future Value of an Annuity with Continuous Compounding (m → ∞)

\[ FV=\frac{PMT}{e^r-1}[e^{rt}-1](1+(e^r-1)T) \]If type is ordinary annuity, T = 0 and we get the **future value of an ordinary annuity with continuous compounding**

otherwise type is annuity due, T = 1 and we get the** future value of an annuity due with continuous compounding**

### Future Value of a Growing Annuity (g ≠ i) and Continuous Compounding (m → ∞)

\[ FV=\frac{PMT}{e^{r}-(1+g)}(e^{nr}-(1+g)^{n})(1+(e^{r}-1)T) \]### Future Value of a Growing Annuity (g = i) and Continuous Compounding (m → ∞)

\[ FV=PMTne^{r(n-1)}(1+(e^{r}-1)T) \]**Cite this content, page or calculator as:**

Furey, Edward "Future Value of Annuity Calculator"; from *http://www.calculatorsoup.com* - Online Calculator Resource.