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.
let the rate be i
24000(1+i)^5 = 34616
(1+i)^5 = 1.44233..
take the 5th root of both sides to get
1+i = .....
isolate i and you are done
To find the effective annual rate of return on Juan's investment over the 5-year period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount after the investment period (the current value of Juan's investment, which is $34,616)
P = initial investment amount (which is $24,000)
r = annual interest rate (which we want to find)
n = number of times interest is compounded per year (let's assume it is compounded once per year)
t = investment period in years (which is 5 years)
We want to solve for r.
Using the values we have:
$34,616 = $24,000(1 + r/1)^(1*5)
Simplifying further:
$34,616/$24,000 = (1 + r)^5
1.44233 = (1 + r)^5
Now, we can take the fifth root of both sides:
(1.44233)^(1/5) = 1 + r
1.0658 = 1 + r
Subtracting 1 from both sides:
r = 0.0658
To convert this into a percentage, we multiply by 100:
r = 6.58%
Therefore, the effective annual rate of return on Juan's investment over the 5-year period is approximately 6.58%.