Time Value Of Money
Time Value of Money
People need to receive a return on today's money (present value) to reach desired financial goals (future value). Further, people desire to borrow money at a lower cost than can be earned with that money. Here are a few examples of applications of principals of the time value of money.
Compound Interest
At such time as interest is paid on a present value (PV), the balance increases to a future value (FV). The next interest payments are now based on the new balance that includes previous interest payments, and so on. This is compound interest and is represented by the formula:
FV = PV * ( 1 + i )n
Where "i" is the interest rate and "n" is number of times interest is paid
The exponent n causes exponential increases in FV over time. For example, $10,000 invested at 6% per year is worth $10,600 after one year, $11,236 after two years, but a seemingly astonishing $42,919 after 25 years. The 25th interest payment alone was $2,429, considerably more than the first interest payment of $600. This is a good example of the exponential growth resulting from compounding.
The problem can also be worked backwards to find that the price of hamburger increased at an average annual 4.4% rate over the 74 years.
Rule of 72
People often think about doubling the money they have. Money invested over time can double and the Rule of 72 is one way easily to estimate the time it will take to accomplish this goal. The Rule of 72 assumes a constant earning and compounding rate. To compute using the rule divide the interest rate into 72 to find the number of years it would take to double money at that interest rate. For example, if one were able to invest at 9% interest, 72/9 = 8 years. Conversely, if a person wants to double his or her money in five years, dividing 72 by 5 shows that one needs to find an interest rate of 14.4%. According to Miranda Marquit in the Personal Finance Corner of AllBusiness.com,...
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