Final answer:
The correct option is d. It will take approximately 3.1 years for $1,700 to reach $2,070 at a 7% simple interest rate, with the closest answer choice being 3 years (d).
Step-by-step explanation:
To calculate how long it will take for $1,700 to grow to $2,070 at a simple interest rate of 7%, we can use the simple interest formula:
I = P × r × t
Where I is the interest earned, P is the principal amount, r is the interest rate (as a decimal), and t is the time in years.
We first calculate the total interest needed to reach $2,070 by subtracting the initial amount ($1,700) from the final amount ($2,070):
I = $2,070 - $1,700 = $370
Now we can plug the values into the simple interest formula:
$370 = $1,700 × 0.07 × t
Divide both sides by ($1,700 × 0.07) to solve for t:
t = $370 / ($1,700 × 0.07)
t = $370 / $119
t ≈ 3.1 years
Based on the available choices, the closest answer to 3.1 years is 3 years, which is choice (d).