Question

25, 000 invested im a bond thst pays 8.2 interest compounded quarterly how long will it take to invest to reach 200,000. Use model A(t)=P(1+r/n)nt.

Answer 1

Step 1

GIven;

`\begin{gathered} A(t)=P(1+(r)/(n))^(nt) \\ P=25000 \\ r=8.2\text{\%} \\ \end{gathered}`
`\begin{gathered} r=(8.2)/(100)=0.082 \\ n=4 \\ A(t)=200000 \end{gathered}`

Required; To find t, the time

Step 2

Find t

`200000=25000(1+(0.082)/(4))^(4t)`
`\begin{gathered} (200000)/(25000)=(25000(1+(0.082)/(4))^(4t))/(25000) \\ \left(1+(0.082)/(4)\right)^(4t)=8 \\ 4t\ln \left(1+(0.082)/(4)\right)=\ln \left(8\right) \\ t=(3\ln\left(2\right))/(4\ln\left((4.082)/(4)\right))=25.61809 \end{gathered}`

Hence, the time it will take will be;

`25.62\text{ years a}pproximately\text{ to 2 decimal places}`