FUTURE VALUE PROBLEMS A future value problem is one where PERIOD 0 1 2 3 we know the cash flow amount we are investing \$100 ? ? ? today and wish to determine how much it will grow to in n periods Example 1 Bob invests \$100 today at 4%.  How much will this investment Answer grow to in one year? Take .04 * 100 and add it to the \$100 =100*(1+.04) 104 Example 2 Bob invests \$100 today at 4%  How much will this investment =100*(1.04)^2 108.16 grow to in 2 years? Example 3 Bob invests \$100 today at 4%.  How much will this investment =100*(1+.04)^3 112.4864 grow to in 3 years? How would you build a Future Value table from the data in Future Value of \$1 Examples 1-3?  Can you fill in the 6% column? Rate Periods 0.04 0.06 MEMORIZE THE GENERAL FORMULA:  FV=PV*(1+i)^n 1 1.04 In the table to the right, Future Value of \$1, the PV is set 2 1.0816 to 1.00. 3 1.124864 PRESENT VALUE PROBLEMS PERIOD 0 1 2 3 A present value problem is one in which we know the future ? \$104 cash flow to be received…but we need to figure out how much to pay for it today to earn a given interest rate. Example 1a.  How much would Bob have to invest today in order to receive a cash flow of \$104 in one year, assuming the interest rate is 4%? Answer Method:  PV = 104 * 1/(1.04)^1 =104 * 1/(1+.04)^1 100 GENERAL FORMULA:    PV = FV* 1/(1+i)^n Example 1b.  How much would Bob have to invest today to =108.16 * 1/(1+.04)^2 100 receive \$108.16 after two years, assuming a 4% interest rate? Example 1c.  How much would Bob have to invest today to =112.4864 * 1/(1+.04)^3 100 receive \$112.48 after 3 years, assuming a 4% interest rate? Using the General Formula above, and setting FV to 1.00, Rate can you fill in the table on the right for the .06 column? Periods 0.04 0.06 1 0.961538 2 0.924556 3 0.888996