Answer:
14.5 years.
Step-by-step explanation:
Given that you invest $150 at 7% interest compounded annually. Now we need to find about in how many years will you have $400. Then round the answer ot the nearest tenth of a year.
So plug the given values into compound interest formula.
[tex]A=P\left(1+r\right)^t[/tex]
[tex]400=150\left(1+0.07\right)^t[/tex]
[tex]\frac{400}{150}=\left(1+0.07\right)^t[/tex]
[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1+0.07\right)^t[/tex]
[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1.07\right)^t[/tex]
[tex]\ln\left(\frac{400}{150}\right)=t\cdot\ln\left(1.07\right)[/tex]
[tex]\frac{\ln\left(\frac{400}{150}\right)}{\ln\left(1.07\right)}=t[/tex]
[tex]14.4967313882=t[/tex]
Which is approx 14.5 years.
