Question 1193550: hi! any help would be very helpful! thank you!
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How much time will be needed for $30,000 to grow to $34,466.45 if deposited at 7% compounded quarterly?
The amount $30,000 will grow to $34,466.45 in___ year(s).
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
How much time will be needed for $30,000 to grow to $34,466.45 if deposited at 7% compounded quarterly?
The amount $30,000 will grow to $34,466.45 in___ year(s).
(Do not round until the final answer. Then round to the nearest tenth as needed.)
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For the amount of $30000, compounded quarterly, the future value formula is
Future Value = 
where n is the number of quarters.
Therefore, our equation to find "n" is
34466.45 =
Divide both sides by 30000
 =  ,
or
1.148881667 =  .
Take logarithm base 10 of both sides
log(1.148881667) = n*log(1.0175)
and find "n" using your calculator
n =  = 7.999994 quarters.
Finally, round this value 7.999994 to the nearest greater integer 8,
in order for the bank was in position to make the last compounding.
ANSWER. 8 quarters, or 8/4 = 2 years.
Solved.
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To see many other similar (and different) solved problems, look into the lesson
- Problems on discretely compound accounts
in this site, and learn the subject from there.
After reading this lesson, you will tackle such problems on your own without asking for help from outside.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Happy learning (!)
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