Calculates the future value of an investment. This is the lump sum or closing balance you will receive back at the end of the investment.

## FV Formula

FV =IF Rate = 0 THEN-Pv - PMT * NperELSE-Pv * (1 + Rate)^{Nper}- PMT * (1 + Rate * Type) *((1 + Rate)^{Nper}- 1)/ Rate

where Type=0 for payments made at the start of the period and Type=1 for payments made at the end of each period.

## Syntax

FV(r, n, c, p, t)

where:

- r: Number: Interest rate per period (Leaf-level time periods are treated as of equal length).
- n: Number: The number of periods
- c: Number: Equal payments paid out each period during the course of the investment term. Payments are recorded as a negative figure or can be zero, in which case all the interest is compounded and included in the lump sum (f) you get at the end. The payments include both an element of interest and an element of capital (optional).
- p: Number: Present value or the initial investment. Cash outflows such as investments are entered as negative numbers. If you are taking out a loan, this is a cash inflow so is entered as a positive number.
- t: Number: 0 or omitted means payments are made at the start of each period, Type=1 or non-zero means payments are made at the end of each period (optional).

## Format

Input Format | Output Format |
---|---|

Rate: Number (percentage) Nper: Number Pmt: Number Pv: Number Type: Number (binary) |
Number |

## Arguments

The function uses the following arguments:

- r: Number: Numeric line item, property, or expression - percentage
- n: Number: Numeric line item, property, or expression
- c: Number: Numeric line item, property, or expression
- p: Number: Numeric line item, property, or expression
- t: Number: Numeric line item, property, or expression - binary

## Constraints

The function has no constraints.

## Excel equivalent

## Example

*Contract 2* involves an initial investment *Pv* of *10000* with a monthly interest *Rate* of *0.7974%* per month. No payments are made during the investment (*PMT* = 0) so all interest is compounded and paid as a lump sum at the end. The future value *FV* is calculated as:

10000 * (1 + r)^{12}= 10000 * (1.007974)^{12}= 11000

*Contract 3* involves the same initial investment *Pv* of *10000* with the same monthly interest rate *Rate* of *0.7974%* per period (equivalent to 10% per annum compound interest) for 12 months. However, this time 12 payments of *300* (*PMT*) are made to the investor at the start of each month (*Type*). These payments are partly interest, partly capital. This means that at the end of the term, the lump sum that is returned to the investor *FV* is just *7238* out of an initial investment of *10000*.