SOLUTION: Ricky Wow invested $20 000 and the interest was compounded bi-monthly. If this sum amounts to $30 000 after 3.5 years, what is the interest rate?

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Question 1137956: Ricky Wow invested $20 000 and the interest was compounded bi-monthly. If this sum
amounts to $30 000 after 3.5 years, what is the interest rate?
Found 3 solutions by ikleyn, josmiceli, greenestamps:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
30000 = 20000%2A%281%2Br%2F24%29%5E%283.5%2A24%29   ====>


30000%2F20000 = %281%2Br%2F24%29%5E84


%281%2Br%2F24%29%5E84 = 3%2F2 = 1.5   ====>


84%2Alog%28%281+%2B+r%2F24%29%29 = log(1.5)


log%28%281+%2B+r%2F24%29%29 = log%281.5%29%2F84 


log%28%281+%2B+r%2F24%29%29 = 0.002096


1+%2B+r%2F24%29 = 10%5E0.002096


1+%2B+r%2F24 = 1.004838  ====>  r%2F24 = 1.004838 - 1 = 0.004838


r = 24*0.004838 = 0.116  (approximately)


ANSWER.  Interest rate is about 0.116 = 11.6% .


CHECK.  20000%2A%281%2B0.116%2F24%29%5E84 = 30011 dollars.


        With the rounding made on the way, the solution and the answer are correct.

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Tutor @greenestamps made a notice explaining that "bi-monthly" means "one time in two months".

So, below I redo my solution in accordance with this meaning.
------------ 

30000 = 20000%2A%281%2Br%2F6%29%5E%283.5%2A6%29   ====>


30000%2F20000 = %281%2Br%2F6%29%5E21


%281%2Br%2F6%29%5E21 = 3%2F2 = 1.5   ====>


21%2Alog%28%281+%2B+r%2F6%29%29 = log(1.5)


log%28%281+%2B+r%2F6%29%29 = log%281.5%29%2F21 


log%28%281+%2B+r%2F6%29%29 = 0.008385


1+%2B+r%2F6%29 = 10%5E0.008385 = 1.019495


1+%2B+r%2F6 = 1.019495  ====>  r%2F6 = 1.004838 - 1 = 0.019495


r = 6*0.019495 = 0.117  (approximately)


ANSWER.  Interest rate is about 0.117 = 11.7% .


CHECK.  20000%2A%281%2B0.117%2F6%29%5E21 = 30002.8 dollars.


        With the rounding made on the way, the solution and the answer are correct, 
        meaning "bi-monthly" as "once per two months" this time.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+=+A%5B0%5D%2A%28+1+%2B+r%2Fn+%29%5E%28n%2At%29+
+30000+=+20000%2A%28+1+%2B+r%2F24+%29%5E%2824%2A3.5%29+
+1.5+=+%28+1+%2B+r%2F24+%29%5E84+
Take the log of both sides
+log%28+1.5+%29+=+84%2Alog%28%28+1+%2B+r%2F24+%29%29+
+.17609+%2F+84+=+log%28%28+1+%2B+r%2F24+%29%29+
+.0020963+=+log%28%28+1+%2B+r%2F24+%29%29+
+1+%2B+r%2F24+=+10%5E.0020963+
+1+%2B+r%2F24+=+1.0048386+
+r%2F24+=+.0048386+
+r+=+.1161+
11.6%
check the math and get another opinion if needed

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note the more common meaning of "bi-monthly" is every two months -- not twice a month.

If that is the problem you want an answer for, use the calculations shown by the other two tutors but replace the "24" (24 times a year; i.e., twice each month) with "6" (6 times a year; i.e., once every two months).