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svetlana [45]
3 years ago
13

Consider a $100 investment earning 12% compounded quarterly. how long will it take to triple your money? round your answer to th

e nearest tenth of a year.
Mathematics
1 answer:
ANTONII [103]3 years ago
6 0
Summarizing the question,
Principle(P)=$100
Rate (r)=12%=0.12
Amount (A)=3×P=$300
Time=t=?
n=no of times the interest is compouned per year=4
Then,
A=P{(1+r/n)}^(n×t)
or,300=100×{1+0.12/4}^(4×t)
or,300/100=(1+0.03)^(4×t)
or,3=1.03^(4×t)
Taking log on both sides,
log3=log[(1.03)^(4×t)]
or,log3= (4×t)×log(1.03)
or,4t=log3/log(1.03)
or,t=log3/[4×log(1.03)]
or, t=9.29175...
t=9.3 years ANS!!!

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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Part a

Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:

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P(R

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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If we apply this formula to our probability we got this:

P(R

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P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)

And we can find this probability using the complement rule and the normal standard table or excel and we got:

P(z>2.774)=1-P(Z

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