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Question 955652: 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.
Found 3 solutions by lwsshak3, ikleyn, josgarithmetic:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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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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=.04163
r=.02082=2.082%
What was the interest rate as a percent? 2.082%
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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%
CHECK. Future value is  = 231165.26.
Solved correctly.
Answer by josgarithmetic(39838) (Show Source):
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