Question 956874: if $8000 is invested in a 2.5% account for 10 years compounded continuously how long would it take for the account to double?
Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! if $8000 is invested in a 2.5% account for 10 years compounded continuously how long would it take for the account to double?
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Formula for continuous compounding: A=Pe^rt, P=initial investment, r=interest rate, A=amt after t-years.
For given problem:
P=8000
r=.025
t=10 yrs
A=8000e^(.025*10)
A=8000e^(.25)
A≈10272
Amount in account after 10 years≈$10,272
..
doubling the acct:
A/P=2=e^.025t
take log of both sides
.025t*lne=ln2
lne=1
.025t=ln2
t=ln2/.025
t≈28
how long would it take for the account to double? 28 yrs
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
if $8000 is invested in a 2.5% account for 10 years compounded continuously
how long would it take for the account to double?
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In his post, @lwsshak3 gives the answer "28 years".
His calculation formula t =  is correct, and the value which this formula produces is 27.72588722.
So the expected answer is 27.726 years, or 28 years and 265 days, approximately.
It is the expected answer <<<--->>> not 28 years, as it is given in the post by @lwsshar3.
In this problem, we should not round to the closest greater year, because compounding is continuous.
In such problems, it is important to give adequate answers in accordance with the common sense
to demonstrate to the teacher and to all around that you correctly understand the problem.
(In simple terms - to demonstrate that you are not an idiot).
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