The credit card with the transactions described uses the average daily balance method to calculate interest. The monthly interest rate is 1.5% of the average daily balance. Calculate parts a-d using the statement.
| Transaction Description | Transaction Amount |
| :---------------------- | :----------------- |
| Previous balance, $6330.00 | |
| March 1 Billing date | |
| March 5 Payment | $250.00 credit |
| March 7 Charge: Restaurant | $50.00 |
| March 12 Charge: Groceries | $80.00 |
| March 21 Charge: Car Repairs | $280.00 |
| March 31 End of billing period | |
| Payment Due Date: April 9 |
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 $\frac{1}{36}$ 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?
Answer (2)
Calculate the average daily balance: 31 ( $6330 × 4 ) + ( $6080 × 2 ) + ( $6130 × 5 ) + ( $6210 × 9 ) + ( $6490 × 10 ) ≈ $6094.19 .
Calculate the interest: $6094.19 × 0.015 = $91.41 .
Calculate the new balance: $6330 − $250 + $50 + $80 + $280 + $91.41 = $6581.41 .
Calculate the minimum payment: 36 $6581.41 ≈ $182.82 , rounded up to $183 .
Explanation
Calculate the Average Daily Balance First, we need to calculate the average daily balance. This is done by multiplying each daily balance by the number of days it persisted, summing these products, and dividing by the total number of days in the billing cycle (31). The balances are:
Initial balance: $6330.00 (March 1 - March 5, 4 days)
Balance after payment: $6330.00 - $250.00 = $6080.00 (March 5 - March 7, 2 days)
Balance after restaurant charge: $6080.00 + $50.00 = $6130.00 (March 7 - March 12, 5 days)
Balance after groceries charge: $6130.00 + $80.00 = $6210.00 (March 12 - March 21, 9 days)
Balance after car repairs charge: $6210.00 + $280.00 = $6490.00 (March 21 - March 31, 10 days)
So, the average daily balance is calculated as follows:
31 ( $6330 × 4 ) + ( $6080 × 2 ) + ( $6130 × 5 ) + ( $6210 × 9 ) + ( $6490 × 10 )
31 $25320 + $12160 + $30650 + $55890 + $64900 = 31 $188920 ≈ $6094.19
Calculate the Interest Next, we calculate the interest for the month. The monthly interest rate is 1.5%, so we multiply the average daily balance by 0.015:
$6094.19 × 0.015 = $91.41
Calculate the New Balance Now, we calculate the new balance at the end of the billing period. This is the previous balance minus the payment, plus all the charges, plus the interest:
$6330 − $250 + $50 + $80 + $280 + $91.41 = $6581.41
Calculate the Minimum Payment The minimum monthly payment is 36 1 of the balance due at the end of the billing period, rounded up to the nearest whole dollar. So, we calculate 36 1 of the new balance:
36 $6581.41 ≈ $182.82
Rounding this up to the nearest whole dollar, we get $183.
Since the new balance ($6581.41) is greater than $360, the minimum payment is 36 1 of the balance, which we calculated to be $183.
Final Answer Therefore, the minimum monthly payment due by April 9 is $183.
Examples
Credit card companies use the average daily balance to calculate the interest charged to your account. Understanding how this is calculated can help you manage your credit card spending and avoid unnecessary interest charges. For example, making payments earlier in the billing cycle can lower your average daily balance, reducing the amount of interest you owe. This knowledge empowers you to make informed financial decisions and save money.
The minimum monthly payment due by April 9 is calculated to be $183, based on the balance due at the end of the billing period, which includes interest. The new balance was derived from various transactions throughout the month. Since it exceeded $360, the minimum payment was calculated as 36 1 of the balance, rounded up to the nearest whole dollar.
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