Answer:
It will take about 35.439 years to triple.
Step-by-step explanation:
Recall the formula for continuously compounded interest:
[tex]A=P\,e^{r*t}[/tex]
where "A" is the total (accrued or future) accumulated value, "r" is the rate (in our case 0.031 which is the decimal form of 3.1%), "P" is the principal, and "t" is the time in years (our unknown).
Notice also that even that the final amount we want to get is three times $48,000. So our formula becomes:
[tex]3\,*\,48,000=\,48,000\,\,e^{0.031\,*t}\\\frac{3\,*\,48,000}{48,000} =e^{0.031*t}\\3=e^{0.031*t}[/tex]
Now,in order to solve for "t" (which is in the exponent, we use logarithms:
[tex]ln(3)=0.031\,*\,t\\t=\frac{ln(3)}{0.031} \\t=35.439 \,\,years[/tex]
