SOLUTION: Hello, I've been trying to answer the following for a while now and could really use the help: Three years ago Greg invested $1000 at a fixed interest rate compounded every

Question 858982: Hello,
I've been trying to answer the following for a while now and could really use the help:
Three years ago Greg invested $1000 at a fixed interest rate compounded every 6 months. His investment is currently valued at $1400. What is the rate of interest he received? ( Round to 2 decimal places.)
So far I've tried
PV = FV / (1+r/2)n
1400=1000/(1+r/6)6
1.4=(1+r/6)^6
6√1.4=(1+r/6)^6
3.596= (1+r/6)
3.596-1=r/6
2.596=r/6
2.596*6=r
r=15.576131089623319071790108554192
r=15.58
But according to an interest calculator I found online, the answer is actually a bit over 11%. Am I even on the right path? if so, where did I go wrong?
Thank you in advance for your help!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Three years ago Greg invested $1000 at a fixed interest rate compounded every 6 months. His investment is currently valued at $1400. What is the rate of interest he received? ( Round to 2 decimal places.)
------------
3 yrs = 6 compounding periods
r = rate per 6 months
------
1400 = 1000*(1 + r)^6
(1 + r)^6 = 1.4
6*log(1 + r) = log(1.4)
log(1 + r) = log(1.4)/6 =~ 0.024355
1 + r = 10^0.024355
r = 10^0.024355 - 1
r =~ 0.05768 per 6 months
Annual rate = 2*r = 0.11536
= 11.54% per year
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