Answer:
8.96 years
Step-by-step explanation:
You want to know how long it takes for an investment of $3000 at 7% compounded annually to be worth $5500.
The value of an investment P earning compound interest at rate r for t years is ...
[tex]A=P(1+r)^t[/tex]
Using the given values in this formula, we can find t:
[tex]5500 = 3000(1+0.07)^t\\\\\\\dfrac{5500}{3000}=1.07^t\qquad\text{divide by 3000}\\\\\\\log\left(\dfrac{5500}{3000}\right)=t\cdot \log(1.07)\qquad\text{take logarithms}\\\\\\t=\dfrac{\log\left(\dfrac{5500}{3000}\right)}{\log(1.07)}\approx8.9587\qquad\text{divide by the coefficient of t}[/tex]
It will take about 8.96 years for Kim's investment to be worth $5500.