Question 1201799
M wishes to determine how long it will take an initial deposit of $10,000 to double.
Required:
a) If M earns 10% annual interest on the deposit, how long will it take for him to double his money?
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<pre>
For the amount of $10,000, compounded yearly, the future value formula is

    Future Value = {{{10000*(1+0.1)^n}}}

where n is the number of years.



Therefore, our equation to find "n" is

    20000 = {{{10000*1.1^n}}}


Divide both sides by 10000

    {{{20000/10000}}} = {{{1.1^n}}},

or, reducing left side,

    2 = {{{1.1^n}}}.


To solve this equation, take logarithm base 10 of both sides

    log(2) = n*log(1.1)


and find "n" using your calculator

    n = {{{log((2))/log((1.1))}}} = 7.27  years.


Finally, round this value 7.27 to the nearest greater integer 8 (8 years),

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


<U>ANSWER</U>. 8 years.
</pre>

Solved.


Do other part similarly: continue by the same way.


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To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Problems-on-discretely-compound-accounts.lesson>Problems on discretely compound accounts</A> 

in this site, &nbsp;and learn the subject from there.



After reading this lesson, &nbsp;you will tackle such problems on your own without asking for help from outside.



Happy learning (!)



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Hello, when you see the answer from other tutor/tutors to this problem,
not rounded to the whole &nbsp;(integer) &nbsp;number of years, &nbsp;this answer &nbsp;(or such answer) &nbsp;is &nbsp;INCORRECT.


The problem &nbsp;ASSUMES &nbsp;that you round the decimal number of years to the closest greater &nbsp;INTEGER &nbsp;number of years.


Any reasonable person, &nbsp;solving such problems, &nbsp;should understand it as clear
as he &nbsp;(or she) &nbsp;does understand that &nbsp;&nbsp;2 x 2 &nbsp;is &nbsp;4.