Question

You expect to receive $10,000 at graduation in two years. You plan on investing it at 8percent until you have $95,000. How long will you wait from now?Multiple Choice

Answer 1

Given:

Expect to receive = $10000

Rate = 8%

Final amount = $95000

Find-:

How long will you wait

Explanation-:

Value after some time is:

`A=P(1+(r)/(100))^t`

Where,

`\begin{gathered} A=\text{ Future value} \\ \\ P=\text{ Present value} \\ \\ r\text{ = Rate of interest} \\ \\ t=\text{ Time period} \end{gathered}`

So, the value is:

`\begin{gathered} A=95000 \\ \\ P=10000 \\ \\ r=8 \\ \\ \end{gathered}`
`\begin{gathered} A=P(1+(r)/(100))^t \\ \\ 95000=1000(1+(8)/(100))^t \\ \\ (95000)/(10000)=(1+0.08)^t \\ \\ 9.5=1.08^t \end{gathered}`

For time taking log both sides.

`\begin{gathered} \ln9.5=\ln1.08^t \\ \\ (\ln9.5)/(\ln1.08)=t \\ \\ t=29.25 \\ \end{gathered}`

Hence time wait from now:

`=t+2`
`\begin{gathered} =29.25+2 \\ \\ =31.25 \end{gathered}`

So the total time is 31.25 years.