Math Problem Statement

You have a credit card that charges an annual interest rate of 20.1% using the average daily balance method. The table below shows your activity for the month of April.

Date Activity Amount Balance April 1 Beginning Balance 850.00 April 5 Purchase 36.40 886.40 April 11 Payment −200.00 686.40 April 20 Purchase 94.50 780.90 April 23 Purchase 20.00 800.90 April 30 Purchase 63.8 864.7 April 30 Ending Balance 864.7

What is the average daily balance for this account?

$ 790.32 Correct

What is the finance charge for the month of April?

Solution

To calculate the finance charge for April, we use the formula:
Finance Charge=Average Daily Balance×(Annual Interest Rate12)\text{Finance Charge} = \text{Average Daily Balance} \times \left(\frac{\text{Annual Interest Rate}}{12}\right)

Step 1: Compute the monthly interest rate.

Monthly Interest Rate=20.1%12=0.201÷12=0.01675 (or 1.675%)\text{Monthly Interest Rate} = \frac{20.1\%}{12} = 0.201 \div 12 = 0.01675 \text{ (or 1.675\%)}

Step 2: Compute the finance charge.

The given Average Daily Balance is 790.32790.32. Using the formula: Finance Charge=790.32×0.01675\text{Finance Charge} = 790.32 \times 0.01675

Finance Charge=13.23986\text{Finance Charge} = 13.23986

Step 3: Round to two decimal places.

The finance charge for April is: $13.24\boxed{\$13.24}

Let me know if you would like further details or have questions!


Related Questions:

  1. How is the average daily balance method different from other interest calculation methods?
  2. What would the finance charge be if the annual interest rate were 18% instead of 20.1%?
  3. How can paying earlier in the month impact the finance charge?
  4. If you made no payments, how would the finance charge change?
  5. Can you explain how purchases affect the average daily balance?

Tip: To minimize finance charges, pay off as much of the balance as possible before the billing cycle ends.

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Math Problem Analysis

Mathematical Concepts

Finance
Interest Calculation
Average Daily Balance Method

Formulas

Average Daily Balance = (Sum of daily balances) / (Number of days in the billing cycle)
Finance Charge = Average Daily Balance × (Annual Interest Rate / 12)

Theorems

Proportional Calculation of Interest

Suitable Grade Level

Grades 9-12