n = LN(FV / PV) / LN(1 + i)
PV = Present Value
FV = Future Value
i = Discount rate
n = Number of periods
LN = natural logarithm
The lump sum number of periods formula is used to work out the amount of time (n) it takes to grow a lump sum from its present value (PV), to a future value (FV) allowing for a given discount rate (i%).
Lump Sum Number of Periods Formula Excel Function
The Excel NPER function can be used instead of the lump sum number of periods formula, and has the syntax shown below.
*The pmt and type arguments are not used when calculating the number of periods for a lump sum.
If a lump sum of 1,000 is received at the start of period 1, and the discount rate is 10%, then the number of periods to increase the value of the lump sum to 2,000 is given by the lump sum number of periods formula as follows:
n = LN(FV / PV) / LN(1 + i) n = LN(2,000 / 1,000 / LN(1 + 10%) n = 7.27 periods
The same answer can be obtained using the number of periods formula in Excel as follows:
n = NPER(i,,PV,-FV) n = NPER(10%,,1000,-2000) n = 7.27 periods
*don’t forget the minus sign on FV
The lump sum number of periods formula is one of many used in time value of money calculations, discover another at the links below.