The first three questions

Item 2: Rule of 72: (1) Show that if $1000 is invested at 8% interest compounded annually, then it will double in about 9 years. (Note: 9 = 72/8.) (2) Show that if $1000 is invested for 6 years, then it will approximately double in that time if it appreciates at 12% per year. (Note: 12 = 72/6.) Rule of 72 If money is invested at r% interest compounded annually, then it will double in about 72/r years. Alternately, if money is invested for n years, then it will double during that time if it appreciates by about 72% per year. (3) Conclude from the Rule of 72 that for an interest rate of r%, then (1+r/100)72/1 2. Also, conclude that for a number of years, n. (1+.72)" ~ 2. We needn't restrict ourselves to doubling. For instance, the Rule of 114 says that if money is invested at r% interest, then it will triple in about 114/r years. The following table gives the numbers associated with several different multiples. Let's denote the number associated with m by N. That is, N, = 72 and Ng 114. m Number Associated with increasing m-fold 2 72 3 114 1 1.14 5 167 6 186 (4) Notice No = N2 + Ns. Show this is true