Question 1182420
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How long will it take $3,000 to grow to $14,000 if it is invested at 5% compounded monthly?
How many years?
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        In the post by @CPhill, the answer is incorrect.

        In this problem, same as many other similar problems,

        the answer should be expressed in integer number of compounding periods.



<pre>
Principal P = 3000

Amount= 14000

number of compounding = n

compounded 12 times per year

Nominal rate per year = 5%

Effective rate per month  r = 0.05/12

Future value = {{{P*(1+0.05/12)^n}}}

14000 = {{{3000 *( 1 + 0.05/12 )^ n}}}

4.666666667 = {{{(1 + 0.05/12 )^n}}}

log(4.666666667) = {{{n*log((1 + 0.05/12)))}}}

n = {{{log((4.666666667))/(log((1+0.05/12)))}}} = 370.4764986  (approx.)


This decimal number,  370.4764986,  should be rounded up to the closest integer number 371
in order for the bank would be in position to make the last compounding.


<U>ANSWER</U>.  The value at the account first time will exceed $14000 after 371 month, or 30 years and 11 months.
</pre>

Solved correctly, properly and accurately.


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When solving such problems on discrete compounding, always remember that the future value
is NOT a continuous function of time. In opposite, it is piecewise constant function,
which changes its values at the end of each compounding period, ONLY.