Final answer:
To determine the time it will take for a $5,000 investment at 8% annual simple interest to grow to $9,000, the simple interest formula I = PRT is used. The calculation shows that it will take 10 years for the investment to reach $9,000.
Step-by-step explanation:
To calculate how long it will take for an investment of $5,000 at an annual simple interest rate of 8% to grow to $9,000, we use the formula for simple interest, which is I = PRT, where I is the interest, P is the principal amount, R is the rate of interest per year, and T is the time in years.
The total interest earned when the investment is worth $9,000 is $9,000 - $5,000 = $4,000.
Now we can set up the equation: $4,000 = $5,000 x 0.08 x T
Dividing both sides by $5,000 x 0.08 gives us T = $4,000 / ($5,000 x 0.08)
So, T = $4,000 / $400 = 10 years.
Therefore, it takes 10 years for the investment to be worth $9,000.