Final answer:
It will take 7 years for a $5000 investment to grow to $8150 at a 9% annual simple interest rate.
Step-by-step explanation:
To find out how long it takes for an investment to reach a certain amount with a given simple interest rate, we use the formula for calculating simple interest, I = P × r × t. Here, I is the interest earned, P is the principal amount, r is the annual interest rate (written as a decimal), and t is the time in years.
For the given problem, where $5000 is invested at 9% annual simple interest to become worth $8150, we first calculate the total interest earned by subtracting the principal from the final amount: $8150 - $5000 = $3150.
With the interest formula:
I = $3150
P = $5000
r = 0.09 (9% as a decimal)
t = ?
Plugging these values into the formula, we can solve for t:
$3150 = $5000 × 0.09 × t
$3150 = $450 × t
t = $3150 / $450
t = 7 years
It will take 7 years for the investment to grow from $5000 to $8150 at a 9% annual simple interest rate.