(multiplying .95 by itself 15 times yields 46.3 percent.)”
(multiplying .95 by itself 15 times yields 46.3 percent.)”
rate of return:46
assuming returns are reinvested, if the returns over n {\displaystyle n} successive time sub-periods are r 1 , r 2 , r 3 , ⋯ , r n {\displaystyle r_{1},r_{2},r_{3},\cdots ,r_{n}} , then the cumulative return or overall return over the overall time period is the result of compounding the returns together: ( 1 + r 1 ) ( 1 + r 2 ) ⋯ ( 1 + r n ) − 1 {\displaystyle (1+r_{1})(1+r_{2})\cdots (1+r_{n})-1} if the returns are logarithmic returns however, the logarithmic return over the overall time period is: ∑ i = 1 n r l o g , i = r l o g , 1 + r l o g , 2 + r l o g , 3 + ⋯ + r l o g , n {\displaystyle \sum _{i=1}^{n}r_{\mathrm {log} ,i}=r_{\mathrm {log} ,1}+r_{\mathrm {log} ,2}+r_{\mathrm {log} ,3}+\cdots +r_{\mathrm {log} ,n}} this formula applies with an assumption of reinvestment of returns and it means that successive logarithmic returns can be summed, i.e.