document.write( "Question 1081583: Calculate the ROI for the following example and write the value in the space provided.\r
\n" ); document.write( "\n" ); document.write( "Mrs. Green invested $10,000 in mutual fund for a period of 6 years. At the end of 6 years, she received a total amount of $25,000. Calculate the ROI and write the answer in the space provided. \n" ); document.write( "
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she invested 10000 for a period of 6 years.
\n" ); document.write( "at the end of the 6 year period, she has 25000
\n" ); document.write( "the return on her investment is equl to (25000 - 10000) / 10000.
\n" ); document.write( "this would be equal to 15000 / 10000 = 1.5
\n" ); document.write( "the percent return on her investment would be 1.5 * 100 = 150%.
\n" ); document.write( "this does not, however, take into account the time it took to get that return.
\n" ); document.write( "in order to do that, you would want to find the return on investment per year.
\n" ); document.write( "that return would be calculated as follows:
\n" ); document.write( "the general formula would be f = p * (1 + r) ^ n
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the present value
\n" ); document.write( "r is the rate of return each year.
\n" ); document.write( "n is the number of years.
\n" ); document.write( "the formula becomes 25000 = 10000 * (1+r)^6
\n" ); document.write( "divide both sides of this equation by 10000 to get:
\n" ); document.write( "25000/10000 = (1+r)^6
\n" ); document.write( "take the log of both sides of this equation to get:
\n" ); document.write( "log(25000/10000) = log((1+r)^6)
\n" ); document.write( "this is equivalent to log(25000/10000) = 6 * log(1+r)
\n" ); document.write( "divide both sides of this equation by 6 to get log(1+r) = log(25000/10000)/6
\n" ); document.write( "this results in log(1+r) = .0663233348
\n" ); document.write( "this is true if and only if 10^.0663233348 = 1+r
\n" ); document.write( "subtract 1 from both sides of this equation to get:
\n" ); document.write( "10^.0663233348 - 1 = r which results in r = .1649930508
\n" ); document.write( "that would be the return on investment per year.
\n" ); document.write( "to see if this is correct, replace r in the equation of f = p * (1+r)^n to get:
\n" ); document.write( "25000 = 10000 * (1.1649930508)^6 = 25000.
\n" ); document.write( "the overall return on the investment over a period of 6 years is 150%.
\n" ); document.write( "the average return on the investment per year is 16.49930508%
\n" ); document.write( "if you want to round the percent solution to 2 decimal digits, then the average return on the investment per year is 16.50%.\r
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