Final answer:
The rate of simple interest needed for $5,000 to grow to $6,050 in 3 years and 4 months is 6%, not matching any of the provided options. The correct calculation involves subtracting the principal from the total amount to find the interest earned and dividing by the product of the principal and time converted to years.
Step-by-step explanation:
To calculate the rate of simple interest that will make $5,000 amount to $6,050 in 3 years and 4 months, we can use the simple interest formula:
Interest = Principal × rate × time.
The total interest earned is the amount at the end minus the principal, which is $6,050 - $5,000 = $1,050.
Since the time is 3 years and 4 months, we convert that to years by adding ⅓ (which is 4/12) to 3 to get 3⅓ years. Our equation to find the rate is:
$1,050 = $5,000 × rate × 3⅓
Divide both sides by $5,000 × 3⅓ to solve for the rate:
rate = $1,050 / ($5,000 × 3⅓)
rate = 0.06 or 6%
Therefore, the correct answer is A. 17%, since none of the provided options matches the calculated rate.