To illustrate lets compute the amount we would need

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the more risk associated with any situation, the higher the interest rate. To illustrate, let's compute the amount we would need to receive today (the present value) that would be "'alent to receiving $100 one year from now if money can be invested at 10%. We recognize intuitively that, " a 10% interest rate, the present value (the equivalent amount today) will be less than $100. The $100 received - future must include 10% interest earned for the year. Thus, the $100 received in one year (the future value) be l.1O times the amount received today (the present value). Dividing $100/1.1 0, we obtain a present value -S90.91 (rounded). This means that we would do as well to accept $90.91 today as to wait one year and receive _To confirm the equality of the $90.91 receipt now to a $100 receipt one year later, we calculate the future of $90.91 at 10% for one year as follows: $90.91 x 1.10 x 1year = $100 (rounded) To generalize, we compute the present value of a future receipt by discounting the future receipt back to the nt at an appropriate interest rate (also called the discountrate). We present this schematically below: Present Value .- $90.91 Discounted for 1 year at 10% .- Future Value $100 -= either the time period or the interest rate were increased, the resulting present value would decrease. If more than time period is involved, our future receipts include interest on interest. This is called compounding.
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Time Value of Money Tables Appendix A near the end of the book includes time value of money tables. Table I is a present value table that ~ can use to compute the present value of future amounts. A present value table provides present value factors (rnul- tipliers) for many combinations of time periods and interest rates that determine the present value of $1. Present value tables are used as follows. First, determine the number of interest compounding periods involv (three years compounded annually are 3 periods, and three years compounded semiannually are 6 periods). The ex- treme left-hand column indicates the number of periods. It is important to distinguish between years and compound- ing periods. The table is for compouncling periods (years X number of compounding periods per year). Next, determine the interest rate per compounding period. Interest rates are usually quoted on a peryear (an- nual) basis. The rate per compounding period is the annual rate divided by the number of compounding periods per year. For example, an interest rate of 10% peryear would be 10% per period if compounded annually, and 5% pw period if compounded semiannually. Finally, locate the present value factor, which is at the intersection of the row of the appropriate number - compounding periods and the column of the appropriate interest rate per compounding period. Multiply this fac by the dollars that will be paid or received in the future. All values inTable 1are less than 1.0because the present value of $1 received in the future is always smaller tbz; $1.As the interest rate increases (moving from left to right in the table) or the number of periods increases (moving top to bottom), thepresent value factors decline.This illustratestwo importantfacts: (1)present values decline as interes; rates increase, and (2)present values decline as the time lengthens. Consider the following three cases:
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