THE VALUE OF MONEY

The time value of money (TVM) is the concept that a sum of money is worth more now than the same sum will be at a future date due to its earning potential in the interim. Because money can grow when it is invested, a delayed payment is a lost opportunity for growth. The time value of money is a core principle of finance. It is also referred to as the present discounted value.

KEY TAKEAWAYS
The time value of money means that a sum of money is worth more now than the same sum of money in the future.
The principle of the time value of money recognizes that money can grow in value by investing it, and a delayed investment is a lost opportunity.
The formula for computing the time value of money considers the amount of money, its future value, the amount it can earn, and the time frame.
For savings and similar accounts, the number of compounding periods is an important determinant as well.
Inflation has a negative impact on the time value of money because your purchasing power decreases as prices rise.
Understanding the Time Value of Money (TVM)
Most investors would rather receive money today than wait to receive the same amount in the future. That's because a sum of money, once invested, can grow over time. For example, money deposited into a high-yield savings account will earn interest. Over the ensuing months and years, that interest will be added to the principal, earning even more interest. That's what's known as the power of compound interest.


In addition, if money is not invested, its value can erode over time. If you hide $1,000 in a mattress for three years, you will not only lose out on any additional money you could have earned by investing it, but it will have even less buying power than it once did because inflation will have reduced its value.

The concept of the time value of money is often attributed to Martin de Azpilcueta, a Spanish theologian and economist of the 16th century.
1
2

Time Value of Money Formula
The basic time value of money formula doesn't calculate "TVM" itself. Instead, it shows the change in the value of money over a period of time. It calculates the future value of a sum of money based on:

Its present value
Interest rate
Number of compounding periods per year
Number of years
Based on these variables, the TVM formula is:

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�
=
�
�
(
1
+
�
�
)
�
×
�
where:
�
�
=
Future value of money
�
�
=
Present value of money
�
=
Interest rate
�
=
Number of compounding periods per year
�
=
Number of years
​

FV=PV(1+
n
i
​
)
n×t

where:
FV=Future value of money
PV=Present value of money
i=Interest rate
n=Number of compounding periods per year
t=Number of years
​



This allows you to see the difference between the future value and the present value. In most cases, the future value will be higher, which is why it is better to receive that money now rather than at a later date.

The TVM formula may change slightly depending on the situation. For example, in the case of annuity or perpetuity payments, the generalized formula will have additional or fewer factors.

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The time value of money doesn't take into account any capital losses that you may incur or any negative interest rates that may apply. In these cases, you may be able to use negative growth rates to calculate the time value of money
Examples of Time Value of Money
Assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:

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�
=
$
1
0
,
0
0
0
×
(
1
+
1
0
%
1
)
1
×
1
=
$
1
1
,
0
0
0
FV
​

=$10,000×(1+
1
10%
​
)
1×1

=$11,000
​


The formula can also be rearranged to find the value of the future sum in present-day dollars. For example, the present-day dollar amount compounded annually at 7% interest that would be worth $5,000 one year from today is:

�
�
=
[
$
5
,
0
0
0
(
1
+
7
%
1
)
]
1
×
1
=
$
4
,
6
7
3
PV
​

=[
(1+
1
7%
​
)
$5,000
​
]
1×1

=$4,673
​



Effect of Compounding Periods on Future Value
The number of compounding periods has a dramatic effect on the TVM calculations. Taking the $10,000 example above, if the number of compounding periods is increased to quarterly, monthly, or daily, the ending future value calculations are:

Quarterly Compounding:
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�
=
$
1
0
,
0
0
0
×
(
1
+
1
0
%
4
)
4
×
1
=
$
1
1
,
0
3
8
FV=$10,000×(1+
4
10%
​
)
4×1
=$11,038
Monthly Compounding:
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�
=
$
1
0
,
0
0
0
×
(
1
+
1
0
%
1
2
)
1
2
×
1
=
$
1
1
,
0
4
7
FV=$10,000×(1+
12
10%
​
)
12×1
=$11,047
Daily Compounding:
�
�
=
$
1
0
,
0
0
0
×
(
1
+
1
0
%
3
6
5
)
3
6
5
×
1
=
$
1
1
,
0
5
2
FV=$10,000×(1+
365
10%
​
)
365×1
=$11,052

This shows that the TVM depends not only on the interest rate and time horizon but also on how many times the compounding calculations are computed each year.

How Does the Time Value of Money Relate to Opportunity Cost?
Opportunity cost is key to the concept of the time value of money. Money can grow only if it is invested over time and earns a positive return. Money that is not invested loses value over time to inflation. Therefore, a sum of money that is expected to be paid in the future, no matter how confidently its payment is expected, is losing value in the meantime. There is an opportunity cost (the opportunity to invest and earn) to being paid in the future rather than in the present.

Why Is the Time Value of Money Important?
The concept of the time value of money can help guide investment decisions. For instance, suppose a business can choose between Project A and Project B. They are identical except that Project A promises a $1 million cash payout in year one, whereas Project B offers a $1 million cash payout in year five. The payouts are not equal. The $1 million payout received after one year has a higher present value than the $1 million payout after five years.