Online Calculators

# Future Value Formula

Future Value and Annuity Formulas
Type
Formula
1 Future Value of a Present Sum
$FV=PV(1+i)^{n}$ FV = PV * (1 + i)n
2 Future Value of an Annuity
$FV=\dfrac{PMT}{i}((1+i)^n-1)(1+iT)$
2.1 Future Value of an Ordinary Annuity
T = 0
$FV=\dfrac{PMT}{i}((1+i)^n-1)$
2.2 Future Value of an Annuity Due
T = 1
$FV=\dfrac{PMT}{i}((1+i)^n-1)(1+i)$
3 Future Value of a Growing Annuity (g ≠ i)
T = 0 for an ordinary annuity
T = 1 for an annuity due
$FV=\dfrac{PMT}{(i-g)}((1+i)^{n}-(1+g)^{n})(1+iT)$
4 Future Value of a Growing Annuity (g = i)
T = 0 for an ordinary annuity
T = 1 for an annuity due
$FV=PMTn(1+i)^{n-1}(1+iT)$
5 Future Value for Combined Future Value Sum and Cash Flow Annuity
$FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n-1)(1+iT)$
5.1 Future Value for Combined Future Value Sum with an Ordinary Annuity
T = 0
$FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n-1)$
5.2 Future Value for Combined Future Value Sum with an Annuity Due
T = 1
$FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n-1)(1+i)$
6 Future Value for Combined Future Value Sum with Growing Annuity (g < i)
$FV=PV(1+i)^{n}+\dfrac{PMT}{(i-g)}((1+i)^{n}-(1+g)^{n})(1+iT)$
7 Future Value for Combined Future Value Sum with Growing Annuity (g = i)
$FV=PV(1+i)^{n}+PMTn(1+i)^{n-1}(1+iT)$
8 Future Value for Combined Future Value Sum and Annuity including Compounding, Time and Rate
$FV=PV(1+\frac{r}{m})^{mt}+\dfrac{PMT}{\frac{r}{m}}((1+\frac{r}{m})^{mt}-1)(1+(\frac{r}{m})T)$
9 Future Value for Combined Future Value Sum and Annuity with Continuous Compounding (m → ∞)
$FV=PVe^{rt}+\dfrac{PMT}{e^r-1}(e^{rt}-1)(1+(e^r-1)T)$
9.1 Future Value for Combined Future Value Sum and Ordinary Annuity with Continuous Compounding (m → ∞)
$FV=PVe^{rt}+\dfrac{PMT}{e^r-1}(e^{rt}-1)$
9.2 Future Value for Combined Future Value Sum and Annuity Due with Continuous Compounding (m → ∞)
$FV=PVe^{rt}+\dfrac{PMT}{e^r-1}(e^{rt}-1)e^r$
10 Future Value of a Growing Annuity (g ≠ i) and Continuous Compounding (m → ∞)
$FV=\dfrac{PMT}{e^{r}-(1+g)}(e^{nr}-(1+g)^{n})(1+(e^{r}-1)T)$
11 Future Value of a Growing Annuity (g = i) and Continuous Compounding (m → ∞)
$FV=PMTne^{r(n-1)}(1+(e^{r}-1)T)$
• FV = Future Value
• PV = Present Value
• PMT = Payment Amount
• i = interest rate per period (decimal form)
• n = number of periods when compounding is once per period
• n = mt when compounding frequency is different than period frequency
• m = compounding frequency per period
• t = number of periods
• g = interest rate growth per period (decimal form)
• T = Type
• T = 0 for Ordinary Annuity (end)
• T = 1 for Annuity Due (beginning)
• r = interest rate per period in decimal form
• e = Euler's number, a mathematical constant equal to approximately 2.71828

Cite this content, page or calculator as:

Furey, Edward "Future Value Formula"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators