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Unformatted text preview: 1 Appendix: The Time Value of Money: Future Value and Present Value Computations If I deposit $10,000 today, how much will I have for a down payment on a house in five years? Will $2,000 saved each year give me enough money when I retire? How much must I save today to have enough for my childrens college education? The time value of money, more commonly referred to as interest, is the cost of money that is borrowed or lent. Interest can be compared to rent, the cost of using an apartment or other item. The time value of money is based on the fact that a dollar received today is worth more than a dollar that will be received one year from today, because the dollar received today can be saved or invested and will be worth more than a dollar a year from today. Similarly, a dol- lar that will be received one year from today is currently worth less than a dollar today. The time value of money has two major components: future value and present value. Future value computations, which are also referred to as compounding, yield the amount to which a current sum will increase based on a certain interest rate and period of time. Present value, which is calculated through a process called discounting, is the current value of a future sum based on a certain interest rate and period of time. In future value problems, you are given an amount to save or invest and you calcu- late the amount that will be available at some future date. With present value problems, you are given the amount that will be available at some future date and you calculate the current value of that amount. Both future value and present value computations are based on basic interest rate calculations. Simple interest is the dollar cost of borrowing or the earnings from lending money. The interest is based on three elements: The dollar amount, called the principal. The rate of interest. The amount of time. The formula and financial calculator computations are as follows: Interest Rate Basics Interest Rate Basics Formula Financial Calculator* Interest uni003D Principal uni00D7 Rate of interest (annual) uni00D7 Time (years) low due to the insertion ext by the markup in page 35. Please firm if this is fine. Appendix: The Time Value of Money 31 Future Value of a Single Amount The future value of an amount consists of the original amount plus compound interest. This calculation involves the following elements: FV uni003D Future value PV uni003D Present value i uni003D Interest rate n uni003D Number of time periods The formula and financial calculator computations are as follows: Future Value of a Single Amount Formula Table Financial Calculator FV uni003D PV ( 1 uni002B i ) n FV uni003D PV ( Table factor ) PV , I/Y , N , PMT , CPT FV Example C: The future value of $1 at 10 percent after three years is $1.33. This amount is calculated as follows: $1.33 uni003D $ ( 1.001 uni002B 0.10 ) 3 Using Exhibit 1-A: $1.33 uni003D $1.00 ( 1.33 ) 1 PV , 10 I/Y , 3 N , 0 PMT ,...
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