SOLUTION: How long does it take for an amount of money P to double itself if it's invested at 7% interest compounded 4 times a year? Round your answer to 2 decimal places.

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Question 1161309: How long does it take for an amount of money P to double itself if it's invested at 7% interest compounded 4 times a year? Round your answer to 2 decimal places.
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Each compounding period is 7%2F4=1.75 percent rate. 
 PERIODS          BALANCE
 0                  1
 1                  1.0175
 2                  1.035
 .
 .
 .

Must be full 40 compounding periods, or 3 years and 4 months.
or
40%2Aquarters%2A%281%2F4%29%28years%2Fquarters%29=highlight%2810%2Ayears%29


B=P%281.0175%29%5Ex, x number of compound periods
2=1%2A1.0175%5Ex
log%28%282%29%29=x%2Alog%28%281.0175%29%29
x=log%28%282%29%29%2Flog%28%281.0175%29%29
x=39.95
Need the WHOLE number of periods.
x=40quarters-------------------------------

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

How long does it take for an amount of money P to double itself if it's invested at 7% interest compounded 4 times a year? Round your answer to 2 decimal places.
3 years 4 months from the other person is WRONG!. 

You might be able to figure out the correct time, in years! TRY it!!

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

The basic (starting) equation is

    2 = %281%2B0.07%2F4%29%5En

where n is the number of compound periods (quarters).



Take the logarithm base 10 of both sides

    log(2) = n%2Alog%28%281%2B0.07%2F4%29%29

    n = log%28%282%29%29%2Flog%28%281%2B0.07%2F4%29%29 = 39.95 = 40 quartes (rounded).


40 quarters = 10 years.


ANSWER.  10 years.

Solved.

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    - Problems on discretely compounded accounts
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    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


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Free of charge online textbook in ALGEBRA-I
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