SOLUTION: How long (in years) would $600 have to be invested at 11.2%, compounded continuously, to earn $400 interest? (Round your answer to the nearest whole number.)

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Question 1104177: How long (in years) would $600 have to be invested at 11.2%, compounded continuously, to earn $400 interest? (Round your answer to the nearest whole number.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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How long (in years) would $600 have to be invested at 11.2%, compounded continuously, to earn $400 interest?
(Round your answer to the nearest whole number.)
:
The continuous interest formula: A+=+P%2Ae%5E%28rt%29, where:
A = amt after t time
P = initial amt
r = interest rate in decimal form
t = time in years
When we have $400 interest, the accumulated amt: 600+400 = 1000
1000+=+600%2Ae%5E%28.112t%29
we can rewrite it to
600%2Ae%5E%28.112t%29=1000
e%5E%28.112t%29=1000%2F600
reduces to
e%5E%28.112t%29=5%2F3
using natural logs, ln of e is 1 therefore
.112t+=+ln%285%2F3%29
.112t = .5108256
t = .5108256%2F.112
t = 4.56 ~ 5 years to earn $400 interest