Math Problem Statement

The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is

2.52.5​%

of the average daily balance. Calculate parts​ a-d using the statement on the right.

Transaction Description

Transaction Amount

Previous​ balance,

​$6230.006230.00

March 1 Billing date

March 5 Payment

​$300.00300.00

credit

March 7​ Charge: Restaurant

​$60.0060.00

March 12​ Charge: Groceries

​$90.0090.00

March 21​ Charge: Car Repairs

​$270.00270.00

March 31 End of billing period

Payment Due​ Date: April 9

Question content area bottom

Part 1

a. Find the average daily balance for the billing period. Round to the nearest cent.

The average daily balance for the billing period is

​$enter your response here.

​(Round to the nearest cent as​ needed.)

Part 2

b. Find the interest to be paid on April​ 1, the next billing date. Round to the nearest cent.

The interest to be paid on April 1 is

​$enter your response here.

​(Use the answer from part a to find this answer. Round to the nearest cent as​ needed.)

Part 3

c. Find the balance due on April 1.

The balance due on April 1 is

​$enter your response here.

​(Use the answer from part b to find this​ answer.)

Part 4

d. This credit card requires a​ $10 minimum monthly payment if the balance due at the end of the billing period is less than​ $360. ​ Otherwise, the minimum monthly payment is

StartFraction 1 Over 36 EndFraction136

of the balance due at the end of the billing​ period, rounded up to the nearest whole dollar. What is the minimum monthly payment due by April​ 9?

Solution

To calculate the average daily balance and answer each part of the question, we need to consider the daily balances and the number of days each balance is held. Let's go through the problem step by step.


Part 1: Find the average daily balance for the billing period.

  1. March 1–March 4 (4 days): The balance is the previous balance, $6,230.00.

  2. March 5–March 6 (2 days): After a payment of $300, the balance is reduced to $6,230.00 - $300.00 = $5,930.00.

  3. March 7–March 11 (5 days): A restaurant charge of $60 is added, making the balance $5,930.00 + $60.00 = $5,990.00.

  4. March 12–March 20 (9 days): A grocery charge of $90 is added, making the balance $5,990.00 + $90.00 = $6,080.00.

  5. March 21–March 31 (11 days): A car repair charge of $270 is added, making the balance $6,080.00 + $270.00 = $6,350.00.

Now, let's calculate the weighted balance (balance * days held):

Weighted Balance=(6230.00×4)+(5930.00×2)+(5990.00×5)+(6080.00×9)+(6350.00×11)\text{Weighted Balance} = (6230.00 \times 4) + (5930.00 \times 2) + (5990.00 \times 5) + (6080.00 \times 9) + (6350.00 \times 11)

Weighted Balance=24,920+11,860+29,950+54,720+69,850=191,300\text{Weighted Balance} = 24,920 + 11,860 + 29,950 + 54,720 + 69,850 = 191,300

The total number of days in the billing period is 31.

Average Daily Balance=191,30031=6,174.19\text{Average Daily Balance} = \frac{191,300}{31} = 6,174.19

Answer for Part 1:

6,174.19\boxed{6,174.19}


Part 2: Find the interest to be paid on April 1.

The monthly interest rate is 2.52%. To find the interest, we use the formula:

Interest=Average Daily Balance×Interest Rate100\text{Interest} = \text{Average Daily Balance} \times \frac{\text{Interest Rate}}{100}

Substitute the values:

Interest=6,174.19×2.52100=6,174.19×0.0252=155.59\text{Interest} = 6,174.19 \times \frac{2.52}{100} = 6,174.19 \times 0.0252 = 155.59

Answer for Part 2:

155.59\boxed{155.59}


Part 3: Find the balance due on April 1.

To find the balance due, add the interest to the balance at the end of the billing period (March 31 balance of $6,350.00):

Balance Due=6,350.00+155.59=6,505.59\text{Balance Due} = 6,350.00 + 155.59 = 6,505.59

Answer for Part 3:

6,505.59\boxed{6,505.59}


Part 4: Find the minimum monthly payment due by April 9.

The minimum monthly payment is determined as follows:

  • If the balance due is less than $360, the minimum payment is $10.
  • If the balance due is more than $360, the minimum payment is 1/36 of the balance due, rounded up to the nearest dollar.

Since the balance due is $6,505.59:

Minimum Payment=6,505.5936=180.71\text{Minimum Payment} = \frac{6,505.59}{36} = 180.71

Rounding up to the nearest dollar:

Minimum Payment=181\text{Minimum Payment} = 181

Answer for Part 4:

181\boxed{181}


Summary of Answers:

  • Part 1: $6,174.19 (Average Daily Balance)
  • Part 2: $155.59 (Interest to be paid)
  • Part 3: $6,505.59 (Balance due)
  • Part 4: $181 (Minimum monthly payment)

Would you like more details or clarifications? Here are five related questions:

  1. How does the average daily balance method compare to other methods like adjusted balance or previous balance methods?
  2. What would happen to the interest if there were more charges or payments throughout the month?
  3. How would the minimum payment change if the interest rate increased?
  4. How does compounding interest differ in credit card calculations versus loans?
  5. Can paying more than the minimum payment affect the overall interest paid?

Tip: Always aim to pay more than the minimum payment to reduce interest and pay off the balance faster.

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Math Problem Analysis

Mathematical Concepts

Average Daily Balance Method
Interest Calculation
Balance Due
Minimum Payment Calculation

Formulas

Average Daily Balance = (Total of Daily Balances) / (Number of Days)
Interest = Average Daily Balance × (Interest Rate / 100)
Balance Due = Ending Balance + Interest
Minimum Payment = Balance Due / 36 (if over $360) or $10 (if under $360)

Theorems

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Suitable Grade Level

Grades 10-12