Kristin’s credit rating was lowered, and the credit card company raised her - Free 51A

Kristin’s credit rating was lowered, and the credit card company raised her APR from 12% to 13.2%. If her average daily balance this month is x dollars, express algebraically the increase in this month’s finance charges due to the higher APR.

Answer

APR Increase and Finance Charges – Algebraic Expression

Expressing the Increase in Finance Charges Algebraically

When a credit card’s APR (Annual Percentage Rate) increases, the monthly finance charges also increase. This can be calculated using the average daily balance and the monthly periodic rate.

📘 Step 1: Convert APR to Monthly Interest Rate

APR is annual, so we convert it to a monthly rate by dividing by 12:

Monthly rate = APR / 12

Old APR = 12%, so old monthly rate:

r_old = 12% / 12 = 1% = 0.01

New APR = 13.2%, so new monthly rate:

r_new = 13.2% / 12 = 1.1% = 0.011

📊 Step 2: Define Average Daily Balance

Let x = average daily balance in dollars

🧮 Step 3: Express Finance Charges

Old finance charge:

FC_old = 0.01 × x

New finance charge:

FC_new = 0.011 × x

📈 Step 4: Increase in Finance Charge

Increase = FC_new − FC_old
Increase = 0.011x − 0.01x = 0.001x

✅ Final Algebraic Expression:

The increase in this month’s finance charges is 0.001x dollars.

Note: This means the finance charge increases by 0.1% of the average daily balance x.

Detailed Lecture Can Credit Card Companies Raise Interest Rates Due to Credit Rating?

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