Online Calculators

# Future Value of Annuity Calculator

Annuity Future Value Calculator
Interest

Cash Flow (Annuity Payments)

Future Value (FV) of the Growing Ordinary Annuity

\$ 1,288,681.48

## 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 end of each payment period (ordinary annuity, in arrears, 0) or if payments occur at the 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

$$FV=\dfrac{PMT}{i}[(1+i)^n-1](1+iT)$$

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

$$FV=\dfrac{PMT}{i}[(1+i)^n-1]$$

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

$$FV=\dfrac{PMT}{i}[(1+i)^n-1](1+i)$$

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

where g = G/100

$$FV=\dfrac{PMT}{(i-g)}\left[(1+i)^{n}-(1+g)^{n}\right](1+iT)$$

### 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 → ∞)

$$FV=\dfrac{PMT}{e^r-1}[e^{rt}-1](1+(e^r-1)T)$$

If type is ordinary annuity, T = 0 and we get the future value of an ordinary annuity with continuous compounding

$$FV=\dfrac{PMT}{e^r-1}[e^{rt}-1]$$

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

$$FV=\dfrac{PMT}{e^r-1}[e^{rt}-1]e^r$$

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

$$FV=\dfrac{PMT}{e^{r}-(1+g)}(e^{nr}-(1+g)^{n})(1+(e^{r}-1)T)$$

### 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"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators