Final answer:
To determine the principal needed to have $3,000 after 5 years with a 6% simple interest rate, we use the formula for simple interest and solve for the principal. The calculation indicates that the principal should be $2,307.69 when rounded to the nearest cent, although this does not match any of the provided options, suggesting a possible error in the options or the calculation.
Step-by-step explanation:
To calculate the principal needed to reach a future value of $3,000 with simple interest, we use the formula for simple interest: Future Value = Principal + (Principal × interest rate × time). We're given that the future value is $3,000, the interest rate is 6% (or 0.06 as a decimal), and the time is 5 years. Setting up the equation, it looks like this:
$3,000 = Principal + (Principal × 0.06 × 5)
To find the Principal, we need to isolate it on one side of the equation. First, distribute the interest rate and time within the parenthesis:
$3,000 = Principal + (Principal × 0.3)
Combine like terms:
$3,000 = Principal × (1 + 0.3)
$3,000 = Principal × 1.3
Now, divide both sides by 1.3 to solve for the Principal:
Principal = $3,000 / 1.3
Principal = $2,307.69 (rounded to the nearest cent)
Since none of the options given match the correct calculation, the student might need to review the options or the calculation for potential errors.