# Future Value of a Lump Sum Formula

## Formula and Use

The future value of a lump sum formula shows what a cash lump sum received today will be worth in the future.

The formula compounds the value of a lump sum at the start of period 1 (PV), forward to its value at the end of period n (FV). In the formula PV is the value of the lump sum today, i is the discount rate per period, n is the number of periods, and FV is the future value of the lump sum.

## Excel Function

The Excel FV function can be used instead of the FV of a lump sum formula, and has the syntax shown below.

`FV(i, n, pmt, PV, type)`

*The pmt and type arguments are not used when calculating the future value of a lump sum.

## Future Value of a Lump Sum Formula Examples

Example 1

To illustrate, suppose a lump sum of 15,000 is received at the start of period 1. Additionally the discount rate is 5% and the term is 10 periods. The value of the lump sum at the end of the term is given by the FV of a lump sum formula as follows:

```PV = 15,000
i = 5%
n = 10 periods
FV = PV x (1 + i)n
FV = 15,000 x (1 + 5%)10
FV =  24,433.42```

The same answer can be obtained using the future value formula in Excel as follows:

```FV = -FV(i,n,,PV)
FV = -FV(5%,10,,15000)
FV = 24,433.42```

Example 2

To further illustrate, suppose a lump sum of 4,000 is received at the start of period 1. Additionally the discount rate is 3% and the term is 7 periods. The value of the lump sum at the end of the term is given by the FV of a lump sum formula as follows:

```PV = 4,000
i = 3%
n = 7 periods
FV = PV x (1 + i)n
FV = 4,000 x (1 + 3%)7
FV = 4,919.50```

The same answer can be obtained using the future value formula in Excel as follows:

```FV = -FV(i,n,,PV)
FV = -FV(3%,7,,4000)
FV =  4,919.50```

The FV of a lump sum formula is one of many formulas used in time value of money calculations. Discover another at the link below.