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

14.5 years.

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`

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

`\ln\left((400)/(150)\right)=\ln\left(1+0.07\right)^t`

`\ln\left((400)/(150)\right)=\ln\left(1.07\right)^t`

`\ln\left((400)/(150)\right)=t\cdot\ln\left(1.07\right)`

`(\ln\left((400)/(150)\right))/(\ln\left(1.07\right))=t`

`14.4967313882=t`

Which is approx 14.5 years.