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Chapter 4: Problem 3

Lauren did not pay her January FlashCard bill in full, so her February bill has a finance charge added on. The average daily balance is \(\$ 510.44,\) and the monthly periodic rate is 2.5\(\% .\) What should Lauren's finance charge be on her February statement?

Short Answer

Expert verified
Lauren's finance charge on her February statement should be \$12.76.

Step by step solution

01

Convert the Monthly Periodic Rate to a Decimal

To convert the monthly periodic rate from a percentage to a decimal, divide the rate by 100. So the calculation would be \(2.5/100 = 0.025\). This is the decimal equivalent of the monthly periodic rate.
02

Calculate the Finance Charge

The finance charge is calculated by multiplying the Average Daily Balance by the monthly periodic rate. Therefore, Lauren's finance charge for February would be $510.44 multiplied by 0.025. Which is \(510.44 * 0.025 = 12.761\) rounded to the nearest cent is \$12.76.

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Key Concepts

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

Finance Charge Calculation
Calculating finance charges is an important aspect of financial mathematics, especially in understanding credit card statements. A finance charge is an additional fee that a borrower pays on outstanding credit balances. To compute the finance charge, you need two key pieces of information: the average daily balance and the monthly periodic rate. In this case, the finance charge is obtained by multiplying the average daily balance by the monthly periodic rate.
  • The formula is: Finance Charge = Average Daily Balance 脳 Monthly Periodic Rate
  • For Lauren: Finance Charge = \(510.44 \times 0.025\)
  • The calculated finance charge would be \(12.761\), which rounds to \($12.76\)
This simple multiplication gives you the finance charge added to the next bill. Understanding how to calculate fees like these can help manage and predict credit costs effectively.
Average Daily Balance
The average daily balance is a crucial concept for calculating finance charges. It represents the average amount owed per day over a billing cycle. Using this metric ensures that the finance charge reflects any fluctuations in the balance during that time.
  • Calculate each day's balance in a billing period.
  • Add all these daily balances together.
  • Divide by the number of days in the billing period.
This method gives a more accurate charge than using just the end-of-month balance. For Lauren, the given average daily balance was \($510.44\). By understanding the variations in daily balances, you can make more informed financial decisions and manage credit wisely.
Monthly Periodic Rate
The monthly periodic rate is used to determine finance charges on a monthly cycle. It is typically represented as a percentage and indicates what portion of a balance will be added as a finance charge. Understanding this rate helps in knowing how much extra cost will be incurred if a balance isn't paid off in full.
  • Generally derived from an annual percentage rate (APR) by dividing it by 12.
  • Expressed as a decimal for calculations (e.g., 2.5\(\%\) becomes 0.025).
For Lauren, the monthly periodic rate was \(2.5\%\). The point of converting this rate is to simplify calculation processes, allowing the finance charge to be determined easily and accurately.
Decimal Conversion
Decimal conversion is a basic but vital step in financial computations. Often, rates such as interest or periodic rates are given in percentages, which need converting to decimals for ease of multiplication. This step ensures that calculations such as finance charges yield accurate results.
  • Convert percentages to decimals by dividing by 100.
  • Example: \(2.5\%\) to \(0.025\).
  • This decimal format is used in all subsequent calculations.
It's important to understand that this conversion is a standardized approach in financial mathematics, ensuring consistency and precision across various financial calculations. Making this conversion correctly avoids errors in the determination of costs and charges.

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Most popular questions from this chapter

Gary is buying a \(\$ 1,250\) computer on the installment plan. He makes a down payment of \(\$ 150 .\) He has to make monthly payments of \(\$ 48.25\) for 2\(\frac{1}{2}\) years. What is the finance charge?

The policy of the Broadway Pawnshop is to lend up to 35\(\%\) of the value of a borrower's collateral. John wants to use a \(\$ 3,000\) ring and a \(\$ 1,200\) necklace as collateral for a loan. What is the maximum amount that he could borrow from Broadway?

Vincent had these daily balances on his credit card for his last billing period. He did not pay the card in full the previous month, so he will have to pay a finance charge. The APR is 19.2\(\%\) . nine days \(@ \$ 778.12\) eight days \(@ 1,876.00\) four days \(@ 1,112.50\) ten days \(@ 1,544.31\) a. What is the average daily balance? b. What is the finance charge?

Arrange the following lending institutions in descending order according to their APRs for a \(\$ 10,000,\) two-year loan. \(\begin{array}{ll}{\text { East Meadow Savings }} & {9 \frac{1}{2} \%} \\\ {\text { Clinton Park Credit Union }} & {9 \%} \\ {\text { Tivoli Trust }} & {9 \frac{3}{8} \%} \\ {\text { First Bank of Rhinecliff }} & {9.45 \%} \\\ {\text { Columbia Consumer Finance Corp. }} & {9 \frac{9}{16} \%}\end{array}\)

Daniyar paid his April FlashCard with an amount equal to the new purchases shown on his bill. His May bill shows an average daily balance of \(\$ 270.31\) and a monthly periodic rate of 1.95\(\% .\) What is the finance charge on Daniyar's May statement?
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