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Roberta deposited 3,116.92 into savings account with an inteest rate of 3.9% compounded quarterly. About how long will it take for the account to be worth 7,000?

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Answer:

the answer is approximated 83 quarters or 21 years

Step-by-step explanation:

they key in this question is to take into account the word "compounded quarterly" it means that every quarter there is paid
(0.039)/(4)=0.975\%. So the process to obtain the answe is as follows:


3116.92*(1+0.975\%)^(n)=7000

note here that n is the number of quarters needed for accumulating 7.000 using an interest rate of 0.975%, so we proceed with the solution


(7000)/(3116.92)=(1+0.975\%)^(n)


log((7000)/(3116.92))=n*log(1+0.975\%)

Remember here the property of natural logaritm when you apply it to an exponent.


(log((7000)/(3116.92) ))/(log(1+0.975\%)) =n


n=83.38

so the answer is aproximated 83 quarters or 21 years

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