Question 1160547
How long will it take for $600 to double if it is invested at 9% annual interest compounded 3times a year? Enter in exact calculations or round to 3 decimal places.
<pre>For DOUBLING, you go with the following formula: {{{matrix(1,3, 2, "=", (1 + i/m)^(mt))}}}
                           In this case, we get: {{{matrix(3,3, 2, "=", (1 + .09/3)^(3t),
2, "=", 1.03^(3t),
3t, "=", log (1.03, (2)))}}}
                       Time taken to double, or {{{highlight_green(matrix(1,6, t, "=", log (1.03, (2))/3, ",", or, highlight(matrix(1,2, 7.817, years))))}}}

You can check by applying the <b><u>Rule of 72.</b></u>
Since the interest rate of 9% is between 6% and 10%, the RULE of 72 serves as a GREAT estimate of the time it takes for an invested amount to DOUBLE.
This gives us: {{{matrix(1,8, i, "(in", "%", ")", "*", t, "=", 72)}}}  
               {{{highlight_green(matrix(3,3, 9 * t, "=", 72, t, "=", 72/9, t, "=", 8))}}}
As seen, the RULE of 72 estimates that it'll take about 8 years for an investment to DOUBLE, at a 9% ANNUAL interest rate.