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.
To find the effective annual rate of return on Juan's investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (worth) of the investment,
P is the initial principal amount (investment),
r is the annual interest rate (as a decimal),
n is the number of times that interest is compounded per year, and
t is the number of years.
In this case, we know the initial investment (P) is $24,000, the final amount (A) is $34,616, the number of years (t) is 5, and we need to find the annual interest rate (r).
We can rearrange the formula to solve for r:
r = ( (A/P)^(1/(nt)) ) - 1
Substituting the given values:
r = ( ($34,616/$24,000)^(1/(5*1)) ) - 1
r = ( 1.44233^(1/5) ) - 1
Using a calculator or math software, the value of 1.44233^(1/5) is approximately 1.09671.
r = 1.09671 - 1
r ≈ 0.09671
To get the annual interest rate as a percentage, we can multiply by 100:
r ≈ 0.09671 * 100
r ≈ 9.671
So, the effective annual rate of return on Juan's investment over the 5-year period is approximately 9.671%.
To find the effective annual rate of return on Juan's investment over the 5-year period, you can use the formula for compound interest:
Future Value = Present Value * (1 + r)^n
where:
Future Value = $34,616
Present Value = $24,000
r = effective annual rate of return
n = number of years
Let's rearrange the formula to solve for r:
r = (Future Value / Present Value)^(1/n) - 1
Substituting the given values:
r = ($34,616 / $24,000)^(1/5) - 1
r ≈ 0.0702 or 7.02%
Therefore, the effective annual rate of return on Juan's investment over the 5-year period is approximately 7.02%.
solve for r:
24000(1+r)^5 = 34616