Question 955652
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Suppose $20,000 is invested into an account where interest is compounded semiannually. 
After 30 years the balance is $231,165.
What was the interest rate as a percent?
Round the answer to the nearest hundredth of a percent.
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        The answer "2.082%" in the post by @lwsshar3 is incorrect and is FAR from to be true.

        I came to bring a correct solution.



Compound Interest Formula: A=P(1+r/n)^nt, 
P=initial investment, 
r=interest rate, 
n=number of compounding periods per year, 
A=amt after t-years


For given problem:
P=20000
r=interest rate(to be determined)
n=2
t=30
A=amt after 30 yrs
...
231165 = 20000(1+r/2)^2*30
231165/20000 = (1+r/2)^60
11.5583 = (1+r/2)^60
raise both sides to the 1/60th power
1.04163 = 1+r/2
r/2 = 1.04163-1 = 0.0416333
r = 0.0416333*2 = 0.0832667 = 8.32667%, approximately.
What was the interest rate as a percent? 8.32667%


<U>CHECK</U>.  &nbsp;&nbsp;Future value is  &nbsp;&nbsp;{{{20000*(1+0.0832667/2)^60}}} = 231165.26.


Solved correctly.