Question 1209843
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How long do you need to invest your money in an account earning an annual interest rate of 5,624% 
compounded daily so that your investment grows from $1380.96 to $10369  over that period of time? 
give answer in days
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<pre>
The formula for the future value of the deposit compounded daily is

    FV = {{{D*(1+r/365)^n}}},

where n is the number of days.  So we write

    10369 = {{{1380.96*(1 + 0.05624/365)^n}}}.


Divide both sides by  1380.96

    {{{10369/1380.96}}} = {{{(1+0.05624/365)^n}}}.


Simplify

    7.50854478 = {{{(1+0.05624/365)^n}}}.


Take logarithm of both sides

    log(7.50854478) = {{{n*log((1+0.05624/365))}}}


Express n  and calculate

    n = {{{log((7.50854478))/log((1+0.05624/365))}}} = 13085.2 days.


Round it to the closest greater day.


<U>ANSWER</U>.  13086 days.
</pre>

Solved.