Future Value Formula
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
\[ FV=\dfrac{PMT}{i}((1+i)^n1)(1+iT) \]
2.1 Future Value of an Ordinary Annuity
T = 0
T = 0
\[ FV=\dfrac{PMT}{i}((1+i)^n1)\]
2.2 Future Value of an Annuity Due
T = 1
T = 1
\[ FV=\dfrac{PMT}{i}((1+i)^n1)(1+i)\]
3 Future Value of a Growing Annuity (g ≠ i)
T = 0 for an ordinary annuity
T = 1 for an annuity due
T = 0 for an ordinary annuity
T = 1 for an annuity due
\[ FV=\dfrac{PMT}{(ig)}((1+i)^{n}(1+g)^{n})(1+iT)\]
4 Future Value of a Growing Annuity (g = i)
T = 0 for an ordinary annuity
T = 1 for an annuity due
T = 0 for an ordinary annuity
T = 1 for an annuity due
\[ FV=PMTn(1+i)^{n1}(1+iT)\]
5 Future Value for Combined Future Value Sum and Cash Flow Annuity
\[ FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n1)(1+iT)\]
5.1 Future Value for Combined Future Value Sum with an Ordinary Annuity
T = 0
T = 0
\[ FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n1) \]
5.2 Future Value for Combined Future Value Sum with an Annuity Due
T = 1
T = 1
\[ FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n1)(1+i) \]
6 Future Value for Combined Future Value Sum with Growing Annuity (g < i)
\[ FV=PV(1+i)^{n}+\dfrac{PMT}{(ig)}((1+i)^{n}(1+g)^{n})(1+iT)\]
7 Future Value for Combined Future Value Sum with Growing Annuity (g = i)
\[ FV=PV(1+i)^{n}+PMTn(1+i)^{n1}(1+iT)\]
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 → ∞)
\[ FV=PVe^{rt}+\dfrac{PMT}{e^r1}(e^{rt}1)(1+(e^r1)T)\]
9.1 Future Value for Combined Future Value Sum and Ordinary Annuity with Continuous Compounding (m → ∞)
\[ FV=PVe^{rt}+\dfrac{PMT}{e^r1}(e^{rt}1)\]
9.2 Future Value for Combined Future Value Sum and Annuity Due with Continuous Compounding (m → ∞)
\[ FV=PVe^{rt}+\dfrac{PMT}{e^r1}(e^{rt}1)e^r\]
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 → ∞)
\[ FV=PMTne^{r(n1)}(1+(e^{r}1)T)\]
 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