Question 1137956
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<pre>
30000 = {{{20000*(1+r/24)^(3.5*24)}}}   ====>


{{{30000/20000}}} = {{{(1+r/24)^84}}}


{{{(1+r/24)^84}}} = {{{3/2}}} = 1.5   ====>


{{{84*log((1 + r/24))}}} = log(1.5)


{{{log((1 + r/24))}}} = {{{log(1.5)/84}}} 


{{{log((1 + r/24))}}} = 0.002096


{{{1 + r/24)}}} = {{{10^0.002096}}}


{{{1 + r/24}}} = 1.004838  ====>  {{{r/24}}} = 1.004838 - 1 = 0.004838


r = 24*0.004838 = 0.116  (approximately)


<U>ANSWER</U>.  Interest rate is about 0.116 = 11.6% .


<U>CHECK</U>.  {{{20000*(1+0.116/24)^84}}} = 30011 dollars.


        With the rounding made on the way, the solution and the answer are correct.
</pre>

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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.
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<pre>
30000 = {{{20000*(1+r/6)^(3.5*6)}}}   ====>


{{{30000/20000}}} = {{{(1+r/6)^21}}}


{{{(1+r/6)^21}}} = {{{3/2}}} = 1.5   ====>


{{{21*log((1 + r/6))}}} = log(1.5)


{{{log((1 + r/6))}}} = {{{log(1.5)/21}}} 


{{{log((1 + r/6))}}} = 0.008385


{{{1 + r/6)}}} = {{{10^0.008385}}} = 1.019495


{{{1 + r/6}}} = 1.019495  ====>  {{{r/6}}} = 1.004838 - 1 = 0.019495


r = 6*0.019495 = 0.117  (approximately)


<U>ANSWER</U>.  Interest rate is about 0.117 = 11.7% .


<U>CHECK</U>.  {{{20000*(1+0.117/6)^21}}} = 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.
</pre>