SOLUTION: Struggling with this compound interest question. Please help if you can and provide a detailed explanation of how you got the answer.
Joe invested $6000 on Feb 22nd, 2012 into a
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-> SOLUTION: Struggling with this compound interest question. Please help if you can and provide a detailed explanation of how you got the answer.
Joe invested $6000 on Feb 22nd, 2012 into a
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Question 588088: Struggling with this compound interest question. Please help if you can and provide a detailed explanation of how you got the answer.
Joe invested $6000 on Feb 22nd, 2012 into an account earning 3 ¾%
compounded monthly. How many days will it take for his investment to earn
$2000 in interest?
You can put this solution on YOUR website! Joe invested $6000 on Feb 22nd, 2012 into an account earning 3 ¾%
compounded monthly. How many days will it take for his investment to earn
$2000 in interest?
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Compound Interest Formula: A=P(1+r)^n, P=initial investment, r=interest rate per period, n=number of periods, A=amount after n periods.
For given problem:
P=6000
r=.0375/12=.003125
n=what we are to find (how many monthsI
A=amount after n-periods=initial investment +interest=6000+2000=8000
..
8000=6000(1+.003125)^n
8000=6000(1.003125)^n
8000/6000=(1.003125)^n
4/3=(1.003125)^n
take log of both sides:
log(4/3)=nlog(1.003125)
n=log(4/3)/log(1.003125)
using calculator
n=≈92 months≈2766 days (assumed 30 days/mo)
You can put this solution on YOUR website! Joe invested $6000 on Feb 22nd, 2012 into an account earning 3 ¾%
compounded monthly. How many days will it take for his investment to earn
$2000 in interest?
----
A(t) = P(1+(r/n))^(nt)
----
Value will be $8000 at that time.
Note: t days is t/365 years
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8000 = 6000(1+(0.0375/12))^(12(t/365))
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4/3 = (1.0031)^(12t/365)
----
(12t/365) = log(4/3)/log(1.0031)
(12t/365) = 92.94
t = 2827.06 days
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Cheers,
Stan H.
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