SOLUTION: A sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long will it take the investment to grow to $ 400,000?

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Question 1164309: A sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long will it take the investment to grow to $ 400,000?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




Solve for

John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

The formula for this account is

    FV = ,


where FV is the future value and "n" is the number of quarters.



So, you should solve this equation to find n

    400000 = .



First, divide both sides by 250000.  You get

     = ,   or

    1.6 = .


Next, take logarithm base 10 of both sides

    log(1.6) = n*log(1.03).


Hence,  n =  = 15.90 (rounded).


You want to find the number of quarters, which is an integer number.

Therefore, you round the value of 15.90 to the nearest greater integer, where next compounding will happen.


In this way, you get your


ANSWER.  16 quarters,  or 4 years.

Solved.

---------------

To see many other similar 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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