Question

question 2 (multiple choice worth 3 points)
(simple interest and arithmetic sequences lc)

the equation, \\(687.5 = 550(1 + 0.05t)\\), represents the amount of money earned on a simple interest savings account. what does the value 550 represent?

• the value 550 represents the initial balance in the account, which means the account started with $550.
• the value 550 represents the final balance in the account, which means the account balance ended with $550.
• the value 550 represents the final balance in the account, which means the account balance started with $550.
• the value 550 represents the amount of interest earned, which means $550 was added to the initial balance.

Explanation:

Identify the simple interest formula

The standard formula for the total amount \(A\) accumulated with simple interest is:

$$A = P(1 + rt)$$

where:

• \(A\) is the final balance (accrued amount)
• \(P\) is the principal (initial balance)
• \(r\) is the annual interest rate
• \(t\) is the time in years

Map the given equation to the formula

Comparing the given equation \(687.5 = 550(1 + 0.05t)\) to the standard formula \(A = P(1 + rt)\):

• \(A = 687.5\) (the final balance)
• \(P = 550\) (the principal or initial balance)
• \(r = 0.05\) (the interest rate of \(5\%\))
• \(t\) is the time

Determine the meaning of the value 550

The value \(550\) corresponds to \(P\), which represents the initial balance in the account. This means the account started with \(\$550\).

Answer:

• (A) The value 550 represents the initial balance in the account, which means the account started with $550. (Correct answer)
• (B) The value 550 represents the final balance in the account, which means the account balance ended with $550.
• (C) The value 550 represents the final balance in the account, which means the account balance started with $550.
• (D) The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.