Time value of money: interest, compounding, and present value

¶ … Value of Money (TVM) shows how money can grow by earning interest over a period of time, and that money in the present is worth more than money in the future of the same amount. This growth is possible by means of various investment instruments like banks, stock market, insurance, and annuities.

Interest Rates and Compounding

The growth of money is directly proportional to its amount. A small amount will earn only small interest, while larger amounts will earn larger interests. The Interest Rate is the percentage of growth for a given year. Money growth through interest is made possible by investments. Banks, for example, accepts money from its clients through deposits. It then uses this money as loan to other people and make a profit through the transaction. Because of this, the bank also has to pay some compensation to the original depositor, and this is the interest. Simply defined, interest is the cost of borrowing money. There are two types of interest: Simple and Compound. Simple interest is a straightforward percentage value of the principal amount. For example, you invested $100 in a bank that pays 5% interest per year. After 1 year, your money will earn 5% of $100, which is $5. Your total money would be therefore $105. The formula for calculating simple interest is: I = P * r * t where I = Interest amount, P = principal amount, r = interest rate, and t = time. In the example above, the interest value is I = $100 *.05 * 1 = $5 (Garrison 2006).

Compound interest occurs when the principal amount that has had previously accumulated interest grows in proportion with those accumulated interests. In other words, compound interest allows the principal and the subsequent interest earnings to earn more interest. In the example above, let's say that you continued to invest your money for 1 more year. Since we already had $105 after 1 year, we are going to have $105 + $5.25 (5% of $105) = $110.25. We can clearly see that the $5 interest income we got after 1 year has earned an additional $0.25 after the 2nd year (Garrison 2006). Compound interest makes money grow larger over time.

2. Present Value (of a future payment received)

The present value of money is the opposite concept behind TVM. It says that future money is not worth as much as present money (of the same amount). This is because present money has the potential to accumulate interest. For example, if you have $10,000 today and invest it at a rate of 4.5% per annum, you will receive $10,450 after the 1st year ($10,000 + 4.5% of $10,000). On the 2nd year, you will have $10,920.25 ($10,450 + 4.5% of $10,450). On the 3rd year, you will have $11,411.66 ($10,920.25 + 4.5% of $10,920.25). Therefore, the $10,000 that you have today will be worth $11,411.66 after 3 years (Croome 2003). The present value of money shows us that money we have in the present has a large potential for growth, and worth a lot more than money of the same amount in the future.

3. Future Value (of an investment)

The future value of money is the amount that it will grow to after a specified time in the future. In the previous example, the future value of $10,000 after 1 year is $10,450. In the 2nd year, the future value is $10,920.25. In the 3rd year, the future value is $11,411.66. Let's say we want to get $10,000 after 3 years (future value). Assuming that the interest rate is still 4.5%, the money that we should have right now (present value) should be $8,762.97. We can see this in the following computations:

After 1st year: $8,762.97 + 4.5% = $9,157.30

After 2nd year: $9,157.30 + 4.5% = $9,569.38

After 3rd year: $9,569.38 + 4.5% = $10,000

This further illustrates the fact that the same $10,000 in the future (3 years from now) is only worth $8,762.97 in the present (Croome 2003).

5. Annuities and the Rule of '72

At any given interest rate, it will take a specified time for your money to double. How long this time takes is usually a subject of interest for investors. The Rule of 72 is used to determine how long it will take to double your money at a given interest rate. If the interest rate is 100%, your money will be doubled within a year. For other rates, it will take some complex computation due to compounding. In order to avoid this tedious computation, a reasonable estimate can be achieved by dividing 72 by the interest rate. The resulting value would show the number of years it will take to double your money. For example, if you invested your capital in mutual funds where the average growth rate is 10% per annum, it will take 72/10 = 7.2 years for your investment to double its value.

Bibliography:

Garrison, Sharon (2006). StudyFinance.com. "Time Value of Money" Retrieved November 10, 2006 at http://www.studyfinance.com/lessons/timevalue/index.mv

Croome, Shauna (August 27, 2003). "Understanding the Time Value of Money" Retrieved November 10, 2006 at http://www.investopedia.com/articles/03/082703.asp

Wikipedia contributors (2006). "Opportunity cost." Wikipedia, The Free Encyclopedia. Retrieved November 10, 2006 at http://en.wikipedia.org/wiki/Opportunity_cost

Wikipedia contributors (2006). "Rule of 72." Wikipedia, The Free Encyclopedia. Retrieved November 10, 2006 at http://en.wikipedia.org/wiki/Rule_of_72