Question

A person invests $9000 at 3% interest compound annually for 4 years and then invests the balance (the $9000 plus the interest earned) in an account at 7% interest for 8 years. find the final value of the investment.

Answer 1

$17,404.5

Step-by-step explanation:

To calculate the balance after t years, we can use the following equation:

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

Where P is the initial investment and r is the rate.

So, we can calculate the balance after 4 years, replacing t by 4, r by 3%, and P by $9000. Therefore the balance is:

`\begin{gathered} A=9000(1+0.03)^4 \\ A=9000(1.126)_{} \\ A=10129.579 \end{gathered}`

Now, we can use this quantity to calculate the final value of the investment. So, replacing P by 10129.579, r by 7%, and t by 8 years, we get:

`\begin{gathered} A=10129.579(1+0.07)^8 \\ A=10129.579(1.718) \\ A=17404.503 \end{gathered}`

Therefore, the final value of the investment is $17,404.5