Problem

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 $\mathrm{I}=\mathrm{Prt}$, where $\mathrm{r}$ is the monthly rate, $\mathrm{t}$ is one month, and $\mathrm{P}$ is the balance due. Choose the correct answer below. A. The statement is false. A true statement is "Interest on a credit card is calculated using I=Prt, where $\mathrm{r}$ is the annual percentage rate, $t$ is one month, and $\mathrm{P}$ is average daily balance." B. The statement is false. A true statement is "Interest on a credit card is calculated using I=Prt, where $\mathrm{r}$ is the annual percentage rate, $\mathrm{t}$ is one month, and $\mathrm{P}$ is balance due." C. The statement is false. A true statement is "Interest on a credit card is calculated using I=Prt, where $r$ is the monthly rate, $\mathrm{t}$ is one month, and $\mathrm{P}$ is average daily balance." D. The statement is true.

Solution

Step 1 :The formula for calculating interest is indeed I=Prt, where I is the interest, P is the principal amount (the initial amount of money), r is the rate of interest, and t is the time. However, the way the rate and the principal amount are defined in the context of credit card interest might vary.

Step 2 :In the context of credit cards, the interest rate is usually expressed as an annual percentage rate (APR), not a monthly rate. The principal amount (P) is typically the balance due on the credit card.

Step 3 :Therefore, the statement in the question seems to be false because it defines r as the monthly rate instead of the annual rate.

Step 4 :Option A: This option defines r as the annual percentage rate, t as one month, and P as the average daily balance. This seems to be a correct definition because some credit card companies calculate interest based on the average daily balance.

Step 5 :Option B: This option defines r as the annual percentage rate, t as one month, and P as the balance due. This also seems to be a correct definition because some credit card companies calculate interest based on the balance due.

Step 6 :Option C: This option defines r as the monthly rate, t as one month, and P as the average daily balance. This seems to be incorrect because the interest rate is usually expressed as an annual rate, not a monthly rate.

Step 7 :Option D: This option states that the original statement is true, which seems to be incorrect because the original statement defines r as the monthly rate instead of the annual rate.

Step 8 :Therefore, both options A and B seem to be correct. However, without knowing the specific method a credit card company uses to calculate interest, it's hard to say which one is the most accurate.

Step 9 :Final Answer: The statement is false. A true statement could be either \(\boxed{\text{'Interest on a credit card is calculated using I=Prt, where r is the annual percentage rate, t is one month, and P is average daily balance.'}}\) or \(\boxed{\text{'Interest on a credit card is calculated using I=Prt, where r is the annual percentage rate, t is one month, and P is balance due.'}}\)

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