Economics and The Time Value of Money - Time Value of Money: Present and Future Value

A dollar received today is worth more than a dollar received yesterday. That is the essence of the time value of money. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

It is essential to understand the time value of money concepts and formulas presented below, but reliance on the formulas alone is not realistic to pass the CFP exam. Exam takers also must master the use of a financial calculator to have any realistic chance of passing the exam.

There are several different brands of financial calculators available on the market, but the financial calculator of choice for CFP exam takers is the HP 12C by Hewlett Packard.

Understanding the Time Value of Money

Present value
The amount that a future lump sum is worth today given a specified rate of return.

An investment that earns 10% per year and can be redeemed for $1,000 in five years would have a present value of $620. In other words, $620 today is worth $1,000 in five years.

PV = FV / (1 + i)n
FV = future value
PV = present value
I = interest rate
N = compounding period

Future value
The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.

FV = PV(1+i)n

FV = future value
PV = present value
I = interest rate
N = compounding period

Consider the following example:

$1000 invested for 5 years at 10%, compounded annually has a future value of $1,610.51.

FV = $1,000(1+.10)5
= $1,000(1.10)5
= $1,610.51
Ordinary annuity, Annuity Due and Net Present Value
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