Juan invested $24,000 in a mutual fund 5 years ago. Today his investment is worth $34,616. Find the effective annual rate of return on his investment over the 5-year period.
just solve for r in
24000(1+r)^5 = 34616
To find the effective annual rate of return on Juan's investment over the 5-year period, we can use the formula:
Effective Annual Rate of Return = (Ending Value / Beginning Value)^(1 / Number of Years) - 1
In this case, Juan's beginning value is $24,000 and his ending value is $34,616. The number of years is 5. Plugging these values into the formula:
Effective Annual Rate of Return = (34,616 / 24,000)^(1 / 5) - 1
To simplify the calculation, let's break it down into steps:
Step 1: Calculate the fraction: 34,616 / 24,000 = 1.44233
Step 2: Calculate the exponent: 1 / 5 = 0.2
Step 3: Raise the fraction to the power of the exponent: 1.44233^0.2 = 1.0972
Step 4: Subtract 1: 1.0972 - 1 = 0.0972
Step 5: Multiply by 100 to convert to a percentage: 0.0972 * 100 = 9.72%
Therefore, the effective annual rate of return on Juan's investment over the 5-year period is 9.72%.