Question 1158423
The formula for continuous compounding is {{{FV=Pe^(Yr)}}}, where e=2.71828... and P is the amount you invest at the beginning. So we have {{{1500=750*e^(0.08Y)}}}. {{{e^(0.08Y)=2}}}. Taking the natural logarithm of both sides gives {{{ln(e^(0.08Y))=ln(2)}}} {{{0.08Y=ln(2)}}}. {{{Y=ln(2)/0.08}}}. Using a calculator to approximate, we have {{{Y=8.66}}}. It will take about 8.66 years for the investment to double.