Future Value
Future Value (FV) refers to the amount of cash to be received or paid at a future date.
Single-period
Potential investments offer a rate of return of 9% per period. Given an initial investment of $2,000 how much cash would be available at the end of one period?
The investment will return the principal $2,000 plus 9% of $2,000 or $2,180 which is calculated as follows:
FV = (1,000 + 1,000 * 0.09) = 1,000 (1 + .09) = 1,000 (1.09) = 1,090
The FV for one period is:
FV = initial investment * (1 + interest rate)
The equation is: FV = PV (1 + r)
where, FV = Future value
PV = Present value
r = Periodic rate of return
Multi-period
To continue with the above example what will the investment be worth after four periods assuming that the accrued amount can be reinvested at a rate of 9%?
FV = 1,000 * 1.09 * 1.09 * 1.09 * 1.09
= 1,090 * 1.09 * 1.09 * 1.09 = 1188.10* 1.09 * 1.09 = 1295.03 * 1.09
= 1411.58
After four periods the value of the investment will be $1411.58. Although the above method correctly calculates the future value, it is inefficient because you need to multiply $1,000 with 1.09 four times. What if the investment was for 50 periods instead of 4?
We can simplify the equation by using exponents, as shown:
FV = 1,000 * (1.09)4 = 1,000 * (1.41158) = 1411.58
To calculate the FV for multiple periods, the equation is given by:
FV = initial investment * (1 + interest rate) time or
FV = PV (1 + r) n
where, n = number of periods
Example: Albert plans to retire in 15 years. Will he be able to afford a $200,000 condominium when he retires if he invests $100,000 in a 15-year certificate of deposit (CD) that pays 6% interest, compounded annually?
Solution: Yes, he will be able to purchase the condominium because he should have $100,000 (1.06)15 = 239,655.82 when he retires.
You can solve this problem in several ways:
Using the formula and a scientific calculator
Using a financial calculator
Using an Excel spreadsheet
Using a financial calculator:
Input: PV = $100,000
I = 6
N = 15
PMT = 0
Compute: FV = $239,655.82
Note: Financial calculators use built-in sign conventions. So the answer may be $239,655.82. Cash inflows are represented by a plus sign and cash outflows are represented by a minus sign. Albert invests $100,000 in the CD, and this is a cash outflow. The result will be a positive value because Albert will receive that amount.