Final answer:
After investing $1500 in an account with a monthly interest rate of 2.1% for 12 months, using the compound interest formula, the final amount is approximately $1624.82, which corresponds to option A.
Step-by-step explanation:
To determine how much money you will have after 12 months if you invest $1500 in an account that grows at a rate of 2.1% every month, you can use the formula for compound interest. The formula for compound interest is 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 in years.
Since the interest in this problem is compounded monthly, the formula is adjusted to account for monthly compounding: A = P(1 + r)^t, where r = 0.021 and t = 12. Plugging the values into the formula gives us A = $1500(1 + 0.021)12. Through calculation, we find that A ≈ $1624.82, which is option A.
To calculate the amount of money you will have after 12 months, we can use the formula for compound interest. The formula is: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this scenario, P = $1500, r = 2.1%, n = 12 (monthly compounding), and t = 1 year. Plugging in these values, we get: A = $1500(1 + 0.021/12)^(12*1). Calculating this gives us approximately $1,704.81. Therefore, the correct answer is B: $1,704.81.