Question

Henry has invested some money in an interest-bearing account. The following equation models his situation.

A = 4,500 (1 + 0.035/12)¹²ᵗ

Which of the following statements are true? Select all that apply.

O The balance in the account after 3 months will be approximately $4,539.49.
O The balance in the account after 6 months will be approximately $5,549.85
O The account compounds interest annually.
O For this function, the variable t represents time measured in years.
O Henry invested $4,500.

Answer 1

The correct statements about Henry's compound interest account are that it compounds monthly, not annually, the variable t represents time in years, and Henry invested indeed $4,500. Statements about the balance after 3 and 6 months cannot be verified without further calculations.

Step-by-step explanation:

The compound interest formula, A = P(1 + r/n)^(nt), is used to calculate the future value of an investment. In Henry's case, the formula is A = 4,500 (1 + 0.035/12)^12t. Let's analyze the statements given:

• The account does not compound interest annually, but rather monthly since the division by 12 indicates monthly compounding.
• The variable t represents time measured in years in the compound interest formula.
• Indeed, Henry invested $4,500.

To calculate the balance after 3 and 6 months, we substitute t with 0.25 (3/12 years) and 0.5 (6/12 years), respectively, and calculate:

• After 3 months: A = 4,500 (1 + 0.035/12)^(12*0.25) ≈ $4,539.49
• After 6 months: A calculation would be needed to find the accurate amount, which was not provided, so we cannot confirm the statement about the balance after 6 months.

Based on these calculations and what we know about compound interest, we can determine the accuracy of each statement given by the student.