Question

If your invest $150 at 7% interest compounded annually,in how many years will you have $400?. Give your answer of the nearest tenth of a year?

Answer 1

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.

$A=P\left(1+r\right)^t$

$400=150\left(1+0.07\right)^t$

$\frac{400}{150}=\left(1+0.07\right)^t$

$\ln\left(\frac{400}{150}\right)=\ln\left(1+0.07\right)^t$

$\ln\left(\frac{400}{150}\right)=\ln\left(1.07\right)^t$

$\ln\left(\frac{400}{150}\right)=t\cdot\ln\left(1.07\right)$

$\frac{\ln\left(\frac{400}{150}\right)}{\ln\left(1.07\right)}=t$

$14.4967313882=t$

Which is approx 14.5 years.