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Helene's credit card has an APR of 16.8\(\%\) . She never pays her balance in full, so she always pays a finance charge. Her next billing cycle starts today. The billing period is 30 days. Today's balance is \(\$ 712.04\) . She is only going to use the credit card this month to make a \(\$ 5,000\) down payment on a new car. a. If she puts the down payment on the credit card today, what will her daily balance be for each of the 30 days of the cycle? b. Find her average daily balance for the 30-day period if she puts the down payment on the credit card today. c. Find the finance charge for this billing period based on the average daily balance from part a. d. Find her average daily balance for the 30-day period if she puts the down payment on the credit card on the last day of the billing cycle. e. Find the finance charge on the average daily balance from part d. f. How much can Helene save in finance charges if she makes the down payment on the last day, as compared to making it on the first day?

Step by step solution

01

Calculate Daily Balance

To calculate the daily balance for each day of the cycle, we first need to take into account that Helene already has a balance on her card of $712.04 and she makes a down payment of $5,000 today. So, the new balance on her card for each of the 30 days will become $5,000 + $712.04 = $5,712.04. Since she makes no other transactions during this period, her daily balance remains the same.

02

Compute Average Daily Balance for 30-day cycle

The average daily balance is the sum of each day's balance divided by the number of days in the billing cycle. As the balance remains the same each day, it's simply the daily balance multiplied by 30 and divided by 30. Hence, the average daily balance is $5,712.04.

03

Find Finance Charge for the Billing Period

To find the finance charge for the billing period, we multiply the average daily balance by the daily periodic rate, which is the APR divided by 365, and then multiplied by the number of days in the billing cycle. So, the finance charge = $5,712.04 * (16.8% / 365) * 30.

04

Calculate Average Daily Balance if Down Payment Is Made on Last Day

If Helene makes the down payment on the last day of the billing cycle, her balance for the first 29 days will be $712.04 and $5,712.04 on the 30th day. So, to calculate her average daily balance, we add up all the daily balances and divide by 30.

05

Find Finance Charge Based on Average Daily Balance from Step 4

Now, we'll find the finance charge by multiplying the average daily balance obtained from Step 4 by the daily periodic rate and number of days in the billing cycle.

06

Compute Savings in Finance Charges

The savings in the finance charge if she makes the down payment on the last day as compared to the first day is simply the finance charge computed in Step 3 subtracted from the finance charge computed in Step 5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Average Daily Balance

The average daily balance is a critical metric when dealing with credit card finance charges. It refers to the sum of your credit card's balance at the end of each day, divided by the number of days in the billing period. This calculation helps determine the amount that is used to calculate finance charges.
For instance, if a balance stays constant every day due to minimal transactions, the average daily balance is simple to compute as the balance itself. However, in scenarios where balances fluctuate due to purchases or payments, you must sum all those daily balances first. Then, divide the total by the number of days in the billing cycle to get an accurate average. This ensures that each day's balance is considered fairly in the computation.

Annual Percentage Rate

The Annual Percentage Rate (APR) is a yearly interest rate expressed as a percentage that applies to your credit card balance. When calculating finance charges, this rate is crucial as it determines how much interest will accrue on any unpaid amount.
Credit card companies typically disclose the APR to inform users of the cost associated with borrowing. It is used to calculate the interest on the balance each day by converting it into what is known as a daily periodic rate. This daily rate is determined by dividing the APR by 365 (days in a year).
High APRs lead to higher finance charges, leading to more costs if the balance isn't fully paid off. Therefore, understanding your credit card's APR helps in managing and predicting finance costs better.

Finance Charge Calculation

Finance charge calculations involve several steps and are essential in managing your credit card costs. To calculate these charges, the average daily balance is multiplied by the daily periodic rate and the number of days in the billing cycle.
Here's how it works:

• First, determine the daily periodic rate by dividing the APR by 365.
• Then, calculate the average daily balance over the billing cycle.
• Finally, multiply the average daily balance by the daily periodic rate and then by the number of days in the cycle to get the finance charge.

By understanding this process, cardholders can actively manage their expenses and potentially act to reduce finance charges by planning expenditures or making timely payments.

Credit Card Billing Cycle

The credit card billing cycle is the period between two statement closing dates. Typically, it lasts between 28 to 31 days during which any transactions made will be recorded on your current bill.
Managing a credit card involves understanding these cycles because each cycle presents an opportunity to pay off the owed amount before interest kicks in. It also dictates when you'll receive your credit card statement and when the payment is due.
The cycle starts with a balance carried over from the previous cycle and accumulates charges from purchases, cash advances, or balance transfers. Each day's ending balance forms the basis of the average daily balance, influencing how much you might pay in finance charges. Understanding your cycle helps in planning when to make large payments to save on interest.