Question 1201359
.
Find the time required for an investment of 5000 dollars to grow to 7100 dollars 
at an interest rate of 7.5 percent per year, compounded quarterly.
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<pre>
Use the formula for the quarterly compounded account

    F = {{{A*(1 + r/4)^n}}}     (1)

where

    F = future value
    A = present value (the starting deposit)
    r = annual interest rate expressed as a decimal
    n = number of quarters


For the amount of $5000, compounded quarterly at 7.5%, the future value formula is

    F = {{{5000*(1+0.075/4)^n}}}

where n is the number of quarters.



Therefore, our equation to find "n" is

    7100 = {{{5000*(1+0.075/4)^n}}}


Divide both sides by 5000

    {{{7100/5000}}} = {{{(1+0.075/4)^n}}},

or

    1.42 = {{{1.01875^n}}}.


Take logarithm base 10 of both sides

    log(1.42) = n*log(1.01875)


and find the number of quarters "n" using your calculator

    n = {{{log((1.42))/log((1.01875))}}} = 18.88  quarters.


Finally, round this value 18.88 quarters to the nearest greater integer number 19,

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


<U>ANSWER</U>. 19 quarters, or 4 years and 3 quarters (same as 4 years and 9 months).
</pre>

Solved.


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&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> 

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