Question 429064
Solution:Since the investment was compounding continuously we can write:

{{{A(t)=P*e^(kt),where k is the interest rate,t is the time in years, A(t)=55000

and P=15000 is the initial investment. Substitute in our formula:

{{{55000=15000*e^(18*k)}}}, Divide both sides by 15000

{{{11/3=e^(18*k)}}}Taking the ln of both sides we have:

{{{ln(11/3)=18k}}}, since lne=1

{{{k=ln(11/3)/(18)}}}

k=0.072

Answer: The interest rate is 7.2%