Question

determine whether the following statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. interest on a credit card is calculated using i = prt, where r is the monthly rate, t is one month, and p is the balance due. choose the correct answer below. \\(\bigcirc\\) a. the statement is false. a true statement is \interest on a credit card is calculated using i = prt, where r is the annual percentage rate, t is one month, and p is average daily balance.\ \\(\bigcirc\\) b. the statement is false. a true statement is \interest on a credit card is calculated using i = prt, where r is the monthly rate, t is one month, and p is average daily balance.\ \\(\bigcirc\\) c. the statement is false. a true statement is \interest on a credit card is calculated using i = prt, where r is the annual percentage rate, t is one month, and p is balance due.\ \\(\bigcirc\\) d. the statement is true.

Explanation:

To determine the validity of the statement about credit card interest calculation, we analyze the formula \( I = Prt \) and credit card interest concepts:

1. Understand Credit Card Interest Basics: Credit card interest is typically calculated using the average daily balance (not the balance due) and the monthly rate (or APR converted to monthly). The formula \( I = Prt \) applies where:

• \( P \): Average daily balance (not balance due).
• \( r \): Monthly interest rate (or APR divided by 12).
• \( t \): Time in years (for monthly, \( t=\frac{1}{12} \), but sometimes simplified as 1 month with \( r \) as monthly rate).

1. Evaluate the Options:

• Option A: Incorrectly states \( r \) is APR (should be monthly rate or APR/12) and \( P \) as average daily balance (correct part, but \( r \) is wrong).
• Option B: Correctly identifies the original statement is false. It states \( r \) is monthly rate, \( t \) is 1 month, and \( P \) is average daily balance, which matches credit card interest calculation.
• Option C: Incorrectly uses "balance due" for \( P \) (should be average daily balance) and "APR" for \( r \) (should be monthly rate or APR/12, but the main error is \( P \)).
• Option D: The original statement is false (uses "balance due" instead of "average daily balance"), so D is wrong.

Answer:

B. The statement is false. A true statement is "Interest on a credit card is calculated using \( I = Prt \), where \( r \) is the monthly rate, \( t \) is one month, and \( P \) is average daily balance."