SOLUTION: If P48,000 is invested at the rate of 2.5% compounded quarterly, when will the compound amount be P70,000?

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Question 1173000: If P48,000 is invested at the rate of 2.5% compounded quarterly, when will the compound amount be P70,000?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Under the given condition, the formula for the future value is


    F = 48000%2A%281%2B0.025%2F4%29%5En,


where n is the number of the quarter periods.


So, to answer the question, you need solve this equation


    70000 = 48000%2A%281%2B0.025%2F4%29%5En.


Divide both sides by 48000. you will get 


    %281%2B0.025%2F4%29%5En = 70000%2F48000 = 1.458333.


Take log base 10 of both sides


    n*log(1.00625) = log(1.458333)


    n = log%28%281.458333%29%29%2Flog%28%281.00625%29%29 = use your calculator = 60.555.


So, it requires 60.555 quarters, and to be accurate, you need round it to the closest GREATER integer number

in order for the bank was in position to make the last compounding.


So, the answer is 61 quarters, or 15 years and 3 months.


CHECK.    48000%2A%281%2B0.025%2F4%29%5E61 = 70,194.12 dollars.   ! Correct !

Solved.

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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 (!)