## Use

The lump sum discount rate formula is used to work out the discount rate (i), needed to compound a lump sum from from its present value (PV), to a future value (FV) in a number of periods (n).

## Formula

i = (FV / PV)^{(1 / n)}- 1

**Variables used in the formula**

PV = Present Value

FV = Future Value

i = Discount rate

n = Number of periods

Our lump sum discount rate calculator is available to help when using the above formula.

## Excel Function

The Excel RATE function can be used instead of the lump sum discount rate formula, and has the syntax shown below.

RATE(n, pmt, PV, FV, type, guess)

*The pmt, type, and guess arguments are not used when calculating the discount rate for a lump sum.

## Lump Sum Discount Rate Formula Example

If a lump sum of 1,500 is received at the start of period 1, then the discount rate needed to compound this to 5,000 after 10 periods is given by the lump sum discount rate formula as follows:

i = (FV / PV)^{(1 / n)}- 1 i = (5,000 / 1,500)^{(1 / 10)}- 1 i = 0.1279 or 12.79%

The same answer can be obtained using the discount rate formula in Excel as follows:

i = RATE(n,,PV,-FV) i = RATE(10,,1500,-5000) i = 12.79%

*don’t forget the minus sign on FV

The lump sum discount rate formula is one of many used in time value of money calculations, discover another at the links below.