Reading: Time 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 earnings potential in the interim. The time value of money is a core principle of finance. A sum of money in the hand has greater value than the same sum to be paid in the future. The time value of money is also referred to as the present discounted value.
Investors prefer to receive money today rather than the same amount of money in the future because a sum of money, once invested, grows over time. For example, money deposited into a savings account earns interest. Over time, the interest is added to the principal, earning more interest. That’s the power of compounding interest.
If it is not invested, the value of the money erodes over time. If you hide $1,000 in a mattress for three years, you will lose the additional money it could have earned over that time if invested. It will have even less buying power when you retrieve it because inflation reduces its value.
As another example, say you have the option of receiving $10,000 now or $10,000 two years from now. Despite the equal face value, $10,000 today has more value and utility than it will two years from now due to the opportunity costs associated with the delay. In other words, a delayed payment is a missed opportunity.
The most fundamental formula for the time value of money takes into account the following: the future value of money, the present value of money, the interest rate, the number of compounding periods per year, and the number of years.
Based on these variables, the formula for TVM is:
^period*time period
Let’s assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:
FV is Future Value. 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:
PV is present value.
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:
- Monthly Compounding: FV –
- Daily Compounding:
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.
Check Your Understanding
Answer the question below to see how well you understand the topics covered in the previous section. This short quiz does not count toward your grade in the class, and you can retake it an unlimited number of times.
You’ll have more success on the Self Check if you’ve completed the three Readings in this section.
Use this quiz to check your understanding and decide whether to (1) study the previous section further or (2) move on to the next section.
