What is Time Value of Money?

The pricing and valuation of financial securities, including bonds, stocks, and real asset investments, are best understood in the context of finance principles. 

The time value of money is the math of finance whereby a financial return (e.g., interest) is earned over time by saving or investing money.

In addition to investors requiring compensation or a financial return for lending or investing their financial capital, they also want to be compensated with higher expected returns for taking on more financial risk. 

Higher default risk premiums are required by investors in corporate bonds relative to government bonds because there is a higher likelihood or probability that corporations will miss paying on time their interest and principal payment obligations. 

The ability to diversify away some investment risk through holding diversified portfolios of securities also is important to investors when making investment decisions.

The actions of individuals to seek out undervalued and overvalued investment opportunities contribute to making financial markets reasonably efficient—that is, current prices reflect the underlying intrinsic valuations of real and financial assets. We also know that management objectives may differ from owner objectives. 

The final principle is based on the belief that “reputation matters” and considers the ethical behavior of individuals and organizations as to legal, fair, and honest treatment of others.

Money can increase, or grow, over time if we can save (invest) it and earn a return on our savings (investment). Let’s begin with a savings account illustration. 

Assume you have $1,000 to save, or invest; this is your principal. The present value of a savings or an investment is its amount or value today. For our example, this is your $1,000.

A bank offers to accept your savings for one year and agrees to pay to you an 8 percent interest rate for use of your $1,000. This amounts to $80 in interest (0.08 × $1,000). The total payment by the bank at the end of one year is $1,080 ($1,000 principal plus $80 in interest). 

This $1,080 is referred to as the future value or value after one year in this case. The future value of a savings amount or investment is its value at a specified time or date in the future. In general word terms, we have,

Future value = Present value + (Present value × Interest rate)


Future value = Present value × (1 + Interest rate)

In our example, we have,

Future value = $1,000 + ($1,000 × 0.08) = $1,080


Future value = $1,000 × 1.08 = $1,080

Let’s now assume that your $1,000 investment remains on deposit for two years but the bank pays only simple interest, which is interest earned only on the investment’s principal. In word terms, we have,

Future value = Present value × [1 + (Interest rate) × (number of periods)] For our example, this becomes,

Future value = $1,000 × [1 + (0.08 × 2)] = $1,000 × 1.16 = $1,160

Another bank will pay you a 10 percent interest rate on your money. Thus, you would receive $100 in interest ($1,000 × 0.10), or a return at the end of one year of $1,100 ($1,000 × 1.10) from the second bank. 

While the $20 difference in return between the two banks ($1,100 versus $1,080) is not great, it has some importance to most people. For a two-year deposit that pays simple interest annually, the difference increases to $40. 

The second bank would return $1,200 ($1,000 × 1.20) to you, versus $1,160 from the first bank. If the funds were invested for ten years, we would accumulate $1,000 × [1 + (0.08 × 10)] or $1,800 at the first bank. 

At the second bank, we would have $1,000 × [1 + (0.10 × 10)] or $2,000; a $200 difference. This interest rate differential between the two banks will become even more important when we introduce the concept of compounding.

Of course, today’s interest rates paid by banks and other financial institutions are very low, in part, due to the Fed’s easy monetary policy during the 2007–08 financial crisis and the 2008–09 Great Recession, and since then, in an effort to stimulate economic growth.

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