14.1 Present Value: Measuring the Time Value of Money

Present value is the current worth of a future sum of money or stream of cash flows given a specified rate of return ^[1]. The future value is the value of a current asset at a specified date in the future based on an assumed rate of growth over time ^[2]. Compounding is the process where the value of an investment increases because the earnings on an investment, both capital gains and interest, earn interest as time passes ^[3]. The generalized formula for compound interest is ^[3]:

FV = PV x (1 + ( i / n)) ^ (n x t)
Where:
FV = future value
PV = present value
i = the annual interest rate
n = the number of compounding periods per year
t = the number of years

Example: Assume that an investment of $1 million earns 20% per year. The resulting future value, based on varying number of compounding periods is ^[3]:

Annual compounding (n = 1): FV = $1,000,000 x (1 + (20%/1)) ^ (1 x 1) = $1,200,000
Semi-annual compounding (n = 2): FV = $1,000,000 x (1 + (20%/2)) ^ (2 x 1) = $1,210,000
Quarterly compounding (n = 4): FV = $1,000,000 x (1 + (20%/4)) ^ (4 x 1) = $1,215,506
Monthly compounding (n = 12): FV = $1,000,000 x (1 + (20%/12)) ^ (12 x 1) = $1,219,391
Weekly compounding (n = 52): FV = $1,000,000 x (1 + (20%/52)) ^ (52 x 1) = $1,220,934
Daily compounding (n = 365): FV = $1,000,000 x (1 + (20%/365)) ^ (365 x 1) = $1,221,336

^{Compound Interest [4]}