Question

A principal of $4700 is invested at 4.5% interest, compounded annually. How many years will it take to accumulate $9000 or more in the account?

Answer 1

We will use the formula

`\begin{gathered} A=P(1+r)^t \\ A=9,000 \\ P=4700 \\ r=4.5\%=(4.5)/(100)=0.045 \\ t=? \end{gathered}`

Applying we have

`\begin{gathered} 9,000=4700(1+0.045)^t \\ 9,000=4,700(1.045)^t \\ (1.045)^t=(9,000)/(4,700) \\ (1.045)^t=1.91489361 \\ \end{gathered}`

Taking log we have

`\begin{gathered} log(1.045)^t=log(1.9148361) \\ tlog(1.045)=log(1.9148361) \\ t=(log(1.9148361))/(log(1.045)) \\ t=14.75938 \end{gathered}`

Hence the time is approximately 15 years