Documentation/Calc Functions/FV
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Function name:
FV
Category:
Financial Analysis
Summary:
Calculates the future value of an investment or loan. The finance term "future value" refers to the value of an asset at some future date, assuming a specific rate of return.
FV assumes an investment or loan with the following general characteristics:
- An initial lump sum.
- A number of regular payments/deposits.
- A final sum.
- A constant interest rate.
Some of these characteristics can be ignored by setting relevant function arguments to zero.
Note the key distinction between the FV and FVSCHEDULE functions – the former assumes a fixed interest rate while the latter allows for a series of different interest rates.
Syntax:
FV(Rate; NPER; PMT[; [PV] [; Type]])
Returns:
Returns a real number, which is the future value of the specified investment or loan. The number returned is in the same currency unit as the specified present value and period payment, and by default is formatted in a locale-dependent currency format.
Arguments:
Rate is a real number (expressed as a percentage, such as 2.5%, or a decimal fraction, such as 0.025), or a reference to a cell containing that number, which is the periodic interest rate. It is common for interest rates to be quoted annually and, where necessary, care should be taken to convert such values to be compatible with the length of your payment period.
NPER is a real number, or a reference to a cell containing that number, which is the number of payment periods in the term.
PMT is a real number, or a reference to a cell containing that number, which is the constant payment or deposit made in each period.
PV is a real number, or a reference to a cell containing that number, which is the present value of the investment or loan. If PV is omitted, the function uses the value 0.0. PV must be in the same currency units as PMT.
Type is a logical value, or a reference to a cell containing a logical value, which determines whether the due date is at the beginning or end of a payment period. If Type is set to 0 or FALSE, or is omitted, then the function assumes the end of the payment period. If Type is set to any other value, then the function assumes the start of the payment period.
- If any argument is non-numeric, then FV reports a #VALUE! error.
- FV does not impose any range checks on the values of the Rate, NPER, PMT, and PV arguments.
Additional details:
- In common with several of Calc’s financial functions, FV uses a general model to describe both loans and annuities. This model assumes that an initial lump sum is borrowed or invested, a number of regular payments are made or received, and a final sum is paid or received. A constant interest rate is applied and compounded throughout the term of the investment. This model is expressed by the following equations:
- In the case of a zero interest rate:
- [math]\displaystyle{ PV ~+~ PMT \times n~+~FV~=~0 }[/math]
- In the case of a non-zero interest rate:
- [math]\displaystyle{ PV \times (1+r)^{n} ~+~ PMT \times \frac{\left ( \left ( 1+r \right )^{n} -1\right )}{r}\times \left ( 1+ \left (t \times r \right ) \right )~+~FV~=~0 }[/math]
- where:
- FV = future value
- n = number of payment periods
- PMT = periodic payment value
- PV = present value
- r = periodic interest rate
- t = due date flag (0 when the due date is at the end of each payment period; 1 when the due date is at the beginning of each payment period).
- In the case of a zero interest rate:
- FV assumes the convention that money received is positive, while money paid out is negative.
- For more information about the concept of future value, visit Wikipedia's Future value page.
Examples:
Note that the formatting of the return values given in the following examples assume the English (USA) locale.
| Formula | Description | Returns |
|---|---|---|
=FV(A1; A2; A3; A4) where cell A1 contains the formula =8%/12, cell A2 contains the value 48, cell A3 contains the value 500, and cell A4 contains the value -35000. |
Here the function calculates the future value of an investment that costs 35,000 currency units originally, but pays the investor 500 currency units every month. The future value is the extra cash sum that will be paid to the investor at the end of the four-year investment period. The annual interest rate is assumed to be 8% and the periodic payments are made at the end of each month (this is the default setting for the omitted Type argument). The value returned is 19,973.36 currency units. Note that payments to the investor have a positive value, while payments by the investor are negative. Note also the present value of -35,000 currency units leads to future payments of 43,973.36 currency units and the difference between these two is due to interest accrued during the life of the investment. | $19,973.36 |
| =FV(8%/12; 48; 500; −35000; 1) | Here the function calculates the future value of the same investment as the previous example, except that the non-zero value for the Type argument implies that the periodic payments of 500 currency units occur at the beginning of each month (rather than at the end). The value returned is 19,785.52 currency units and this is the cash sum to be paid to the investor at the end of the four-year investment period. Note that the value returned in this case is slightly less than that of the previous example and this is expected because the value of each periodic payment has less time to accrue interest in this scenario. | $19,785.52 |
| =FV(7%; 20; 1500; −15891) | Here the function calculates the future value of an annuity that costs 15,891 currency units originally, but which pays the investor 1,500 currency units at the end of each year, for the next 20 years. A constant annual interest rate of 7% is assumed. The Type argument is omitted and assumes its default value of 0. FV returns the value -0.08 currency units, and so after receiving 30,000 currency units in annual payments there is no significant residual value at the end of the investment period. | -$0.08 |
| =FV(5.5%/12; 60; −300; 15706) | Here the function calculates the future value of a loan, assuming a constant annual interest rate of 5.5%. The loan of 15,706 currency units is to be repaid at the rate of 300 currency units each month for 5 years. The Type argument is again omitted and assumes its default value of 0. FV returns the value -0.20, and so there is no significant residual value at the end of the loan period. | -$0.20 |
| =FV(7.5%/12; 18*12; −100; −3785.21) | An investment is designed to provide a cash sum in 18 years time. The initial cost of the investment is 3,785.21 currency units and subsequently 100 currency units are to be invested at the end of each month. A constant annual interest rate of 7.5% is assumed. The Type argument is omitted and assumes its default value of 0. FV returns the value 60,000.01, which is the value of the cash sum to be paid to the investor at the end of 18 years. | $60,000.01 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
FV