Question 1196016
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If a simple discount rate of 11% is equivalent to a simple interest rate of 14.5%. 
Then what is the length of time under consideration?
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            In this problem, the most difficult part is to understand what they want from you.

            I will explain it to you in full details.



<pre>
Let B is the borrowed amount, and let R be the amount which should be returned.


Since the simple discount rate is 11%, we have this equation (the definitionm of the simple discount rate) 

    {{{(R-B)/R}}} = 0.11,

which gives 

    R - B = 0.11*R,  or  B = R - 0.11R,  or  B = 0.89R.    (1)


Next, since the loan is simple interest rate of 14.5%, the amount to return at the end is

    R = B + 0.145*B*t,     (2)

where t is the time in years, which is the unknown quantity in this problem.


Substitute B from equation (1) into equation (2).  You will get

    R = 0.89R + 0.145*(0.89*R)*t.


Cancel the factor R in both sides

    1 = 0.89 + 0.145*0.89*t.


Simplify and find t

    1 - 0.89 = 0.12905*t,  or  0.11 = 0.12905*t,  or  t = {{{0.11/0.12905}}} = 0.852383 of an year, 

which is 0.852383*365 = 311.11 days,  which we should round to 311 days.


<U>ANSWER</U>.  The length of the time under consideration is 311 days (rounded).
</pre>

Solved.


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The &nbsp;"solution" &nbsp;by @josgarithmetic is incorrect, &nbsp;illogical and irrelevant.


You better ignore it, &nbsp;for the safety of your mind.