## 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.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.