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INTEREST RATES IN TEXTR00K THEORY

You probably were first introduced to the time value of money in college or in a job training program using equations such as these:

(1.1)

where FV = future value, PV = present value, i = interest rate per time period, and N = number of time periods to maturity.

The two equations are the same and merely are rearranged algebraically. The future value is the present value moved forward along a time trajectory representing compound interest over the N periods; the present value is the future value discounted back to day zero at rate i per period.

In your studies, you no doubt worked through many time-value-of- money problems, such as: How much will you accumulate after 20 years if you invest \$1,000 today at an annual interest rate of 5%? How much do you need to invest today to accumulate \$10,000 in 30 years assuming a rate of 6%? You likely used the time-value-of-money keys on a financial calculator, but you just as easily could have plugged the numbers into the equations in 1.1 and solved via the arithmetic functions.

The interest rate in standard textbook theory is well defined. It is the growth rate of money over time – it describes the trajectory that allows \$1,000 to grow to \$2,653 over 20 years. You can interpret an interest rate as an exchange rate across time. Usually we think of an exchange rate as a trade between two currencies (e.g., a spot or a forward foreign exchange rate between the U.S. dollar and the euro). An interest rate tells you the amounts in the same currency that you would accept at different points in time. You would be indifferent between \$1,741 now and \$10,000 in 30 years, assuming that 6% is the correct exchange rate for you. An interest rate also indicates the price of money. If you want or need \$1,000 today, you have to pay 5% annually to get it, assuming you will make repayment in 20 years.

Despite the purity of an interest rate in time-value-of-money analysis, you cannot use the equations in 1.1 to do interest rate and cash flow calculations on money market securities. This is important: Money market interest rate calculations do not use textbook time-value-of-money equations. For a money manager who has \$1,000,000 to invest in a bank CD paying 3.90% for half of a year, it is wrong to calculate the future value in this manner:

While it is tempting to use N = 0.5 in equation 1.1 for a 6-month CD, it is not the way money market instruments work in the real world.

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