Final answer:
To reach $1,210 in 6 years with an account paying 3.8% interest compounded monthly, Paisley would need to initially invest approximately $947.06, which rounds to $900 to the nearest hundred dollars. However, the answer choices provided in the question appear incorrect as none matches the calculation.
Step-by-step explanation:
To calculate the initial investment Paisley needs to make, we use the formula for the future value of an investment with compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for.
Paisley wants the value of the investment to reach $1,210 in 6 years with an interest rate of 3.8% compounded monthly. First, convert 3.8% to decimal by dividing by 100, which gives 0.038. The interest is compounded monthly, so n is 12. Plugging the values into the formula:
A = P(1 + 0.038/12)^(12*6)
$1,210 = P(1 + 0.038/12)^(12*6)
P = $1,210 / (1 + 0.038/12)^(12*6)
P ≈ $947.06
Since the question asks for the nearest hundred dollars, the correct answer is $900, which is not provided in the given options A) $233.23, B) $305.09, C) $333.83, and D) $443.38. Therefore, there seems to be a discrepancy in the provided options. The calculation indicates the initial investment would be approximately $947, which rounds to the nearest hundred as $900.