Question 1196091
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Please help with the homework:
At what compound interest rate per annum must money be invested 
if the principal must treble in ten years and interest is calculated monthly.
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Let "r" be the compound interest rate per annum.

Start from the formula for the future value

    3 = {{{(1+r/12)^(10*12)}}} = {{{(1+r/12)^120}}}


Take logarithm base 10 of both sides of the equation

    log(3) = 120*log(1+r/12).


Find log(1+r/12) = {{{log((3))/120}}} = 0.00397601.


It gives  1 + r = {{{10^0.00397601}}} = use your calculator = 1.009197137.


Hence,  r/12 = 1.009197137 - 1 = 0.009197137;  then  r = 12*0.009197137 = 0.110365644 = 0.1104 (rounded).


<U>ANSWER</U>.  The needed compound interest rate is about  11%  per annum (rounded).
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Solved.