## Info

0% Interest rate

2 4 6 8 10 12 14 Periods

0% Interest rate

2 4 6 8 10 12 14 Periods could earn on alternative investments of equal risk.) What value of X will make you indifferent between X dollars today or the promise of \$127.63 5 years hence?

Table A.1 shows that the initial amount of \$100 growing at 5% a year yields \$127.63 at the end of 5 years. Thus, you should be indifferent in your choice between \$100 today and \$127.63 at the end of 5 years. The \$100 is the present value, or PV, of \$127.63 due in 5 years when the applicable interest rate is 5%. Therefore, if X is anything less than \$100, you would prefer the promise of \$127.63 in 5 years to X dollars today.

In general, the present value of a sum due n years in the future is the amount that, if it were invested today, would grow to equal the future sum over a period of n years. Because \$100 would grow to \$127.63 in 5 years at a 5% interest rate, \$100 is the present value of \$127.63 due 5 years in the future when the appropriate interest rate is 5%.

Finding present values (or discounting, as it is commonly called) is simply the reverse of compounding, and Equation A.2 can readily be transformed into a present value formula: