<span>She invested 10000 for a period of 6 years. At the end of the 6 year period, she has 25000 The return on her investment is equal to (25000 - 10000) / 10000. This would be equal to 15000 / 10000 = 1.5 The percent return on her investment would be 1.5 * 100 = 150%. this does not take into account the time it took to get that return. in order to do that, you would want to find the return on investment per year. That return would be calculated: The general formula would be f = p * (1 + r) ^ n f is the future value p is the present value r is the rate of return each year. n is the number of years. the formula becomes 25000 = 10000 * (1+r)^6 divide both sides of this equation by 10000 to get: 25000/10000 = (1+r)^6
take the log of both sides of this equation to get: log(25000/10000) = log((1+r)^6) this is equivalent to log(25000/10000) = 6 * log(1+r) divide both sides of this equation by 6 to get log(1+r) = log(25000/10000)/6 this results in log(1+r) = .0663233348 this is true if and only if 10^.0663233348 = 1+r subtract 1 from both sides of this equation to get: 10^.0663233348 - 1 = r which results in r = .1649930508 that would be the return on investment per year. to see if this is correct, replace r in the equation of f = p * (1+r)^n to get: 25000 = 10000 * (1.1649930508)^6 = 25000. the overall return on the investment over a period of 6 years is 150%. the average return on the investment per year is 16.49930508% if you want to round the percent solution to 2 decimal digits, then the average return on the investment per year is 16.50%. </span>
