An investment today of $3,3OO is worth $10,000 IN 8 YEARS. At what rate has your investment been growing(annually) over the eight years ?
For compounding rate of return:
3300*(1+r)^8 = 10000.
so
(1+r)^8 = 10000/3300 = 3.0303
My calculator has a nth root button -- so 1+r=1.14864 so r=14.864%.
(without an nth root button, you can easily get there with successive approximations using something like an EXCL spreadsheet or a hand calculator).
To calculate the annual growth rate of the investment over the eight years, we need to solve the equation:
3300*(1+r)^8 = 10000
First, divide both sides of the equation by 3300 to isolate the term (1+r)^8:
(1+r)^8 = 10000/3300 = 3.0303
To remove the exponent, we need to find the eighth root of both sides. Using a calculator with an nth root function, take the eighth root of 3.0303:
(1+r) = 1.14864
Now, subtract 1 from both sides of the equation:
r = 1.14864 - 1 = 0.14864
Finally, convert the decimal to a percentage by multiplying by 100:
r = 0.14864 * 100 = 14.864%
Therefore, the investment has been growing at a rate of approximately 14.864% per year over the eight-year period.