Question 1205115
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Mia invests $2,000 in a money market account that earns 5% annual interest, compounded continuously. 
Approximately how many years will it take her money to grow to the $4,500 she needs for her small 
business start-up? (Round your answer to one decimal place.)
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<pre>
Using the formula for continuously compounded account, write

    4500 = {{{2000*e^(0.05*t)}}}.


Divide both sides by 2000

    {{{4500/2000}}} = {{{e^(0.05*t)}}}.


It is the same as

    2.25 = {{{e^(0.05*t)}}}.


Take natural logarithm of both sides

    ln(2.25) = 0.05*t,

    t = {{{ln(2.25)/0.05}}} = 16.22


Round to one decimal place

    t = 16.2 years.    <U>ANSWER</U>
</pre>

Solved.


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

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

in this site.


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