In interviewing November's statement she notices that her beginning balance was $600 and that she made a $200 payment on November 10. She also charged purchases of $80 on November, 5, $100 on November 15, and $50 on November 30. She paid $5.27 in interest the month before. She does remember, though, seeing the letters APR and the number 16%. Also, the back of her statement indicating that interest was charged using the average daily balance method, including current purchases, which considers the day of a charge or credit.
a. Find the unpaid balance on November 30 before the interest is charged.
b. Assuming a 30-day period in November find the average daily balance.
c. Calculate the interest for November.
d. What was the unpaid balance for November after interest is charged?
a. The unpaid balance on November 30 before interest is charged can be calculated by subtracting the total payments and charges from the beginning balance:
Unpaid balance on November 30 = Beginning balance - Total payments - Total charges
Unpaid balance on November 30 = $600 - $200 - $80 - $100 - $50
Unpaid balance on November 30 = $170
b. To calculate the average daily balance, we need to sum up the daily balances for each day in November and divide it by the number of days in November.
Average daily balance = (Sum of daily balances) / Number of days
Daily balance is calculated by considering the charges made on that day and the payments made on previous days.
Let's calculate the daily balances:
On November 1: Daily balance = Beginning balance = $600
On November 2 to November 4: Daily balance = Previous day's balance = $600
On November 5: Daily balance = Previous day's balance + Charge on that day
Daily balance on November 5 = $600 + $80 = $680
On November 6 to November 10: Daily balance = Previous day's balance = $680
On November 11: Daily balance = Previous day's balance - Payment made on November 10
Daily balance on November 11 = $680 - $200 = $480
On November 12 to November 14: Daily balance = Previous day's balance = $480
On November 15: Daily balance = Previous day's balance + Charge on that day
Daily balance on November 15 = $480 + $100 = $580
On November 16 to November 29: Daily balance = Previous day's balance = $580
On November 30: Daily balance = Previous day's balance + Charge on that day
Daily balance on November 30 = $580 + $50 = $630
Now, let's calculate average daily balance:
Average daily balance = (Sum of daily balances) / Number of days
Average daily balance = ($600 + $600 + $680 + $680 + $680 + $480 + $480 + $480 + $580 + $580 + $580 + $580 + $580 + $630) / 30
Average daily balance = $12240 / 30
Average daily balance = $408
c. To calculate the interest for November, we need to multiply the average daily balance by the APR (Annual Percentage Rate) and divide it by the number of days in a year. Since November has 30 days, we will use that value.
Interest for November = (Average daily balance * APR) / 365 * Number of days in November
Interest for November = ($408 * 0.16) / 365 * 30
Interest for November = ($65.28) / 365 * 30
Interest for November ≈ $5.80
d. The unpaid balance for November after interest is charged can be calculated by adding the interest to the unpaid balance on November 30:
Unpaid balance after interest = Unpaid balance on November 30 + Interest for November
Unpaid balance after interest = $170 + $5.80
Unpaid balance after interest ≈ $175.80
a. To find the unpaid balance on November 30 before the interest is charged, we need to calculate the total charges and payments up until November 30.
Total charges:
November 5: $80
November 15: $100
November 30: $50
Total charges = $80 + $100 + $50 = $230
Total payments:
November 10: $200
Total payments = $200
Unpaid balance on November 30 before interest is charged = Beginning balance + Total charges - Total payments
Unpaid balance = $600 + $230 - $200 = $630
b. To find the average daily balance for the 30-day period in November, we need to calculate the sum of the daily balances and divide by 30.
There is only one transaction (payment) made on November 10, so the daily balances will be the same for all other days.
Daily balance = Unpaid balance = $630
Average daily balance = Sum of daily balances / Number of days
Average daily balance = ($630 * 30) / 30 = $630
c. To calculate the interest for November, we need to use the formula: Interest = (Average daily balance * APR * Number of days) / 365.
Given:
APR = 16%
Number of days in November = 30
Interest = (Average daily balance * APR * Number of days) / 365
Interest = ($630 * 0.16 * 30) / 365 = $8.22
d. To find the unpaid balance for November after interest is charged, we need to add the interest to the unpaid balance on November 30.
Unpaid balance after interest is charged = Unpaid balance on November 30 + Interest
Unpaid balance = $630 + $8.22 = $638.22
To find the answers to these questions, we need to go step by step.
a. Find the unpaid balance on November 30 before the interest is charged.
To find the unpaid balance on November 30 before the interest is charged, we start with the beginning balance ($600) and subtract any payments or credits (in this case, only the $200 payment made on November 10) and add any new charges (in this case, $80 on November 5, $100 on November 15, and $50 on November 30).
Unpaid balance before interest = Beginning balance - payment + charges
Unpaid balance before interest = $600 - $200 + $80 + $100 + $50 = $630
b. Assuming a 30-day period in November, find the average daily balance.
To find the average daily balance, we will calculate the balance for each day of the month and then take the sum of these balances divided by the number of days in the month (30 in this case).
Here is a step-by-step calculation for the average daily balance:
- First 5 days: $600 (Beginning balance)
- Day 6-10: $600 - $80 = $520 (Deducting $80 charge made on November 5)
- Day 11-14: $520 (No new charges or payments during this period)
- Day 15-29: $520 + $100 - $5.27 (previous month's interest) = $614.73 (Adding $100 charge and deducting the interest)
- Day 30: $614.73 + $50 = $664.73 (Adding $50 charge made on November 30)
Average daily balance = (balance on each day / number of days in the month)
Average daily balance = ($600 x 5 + $520 x 5 + $520 x 4 + $614.73 x 15 + $664.73 x 1) / 30
Average daily balance = ($3000 + $2600 + $2080 + $9220.95 + $664.73) / 30
Average daily balance ≈ $739.41
c. Calculate the interest for November.
To calculate the interest for November, we need to use the average daily balance, the APR of 16%, and the number of days in the month (30).
Interest = (Average daily balance x APR x Number of days) / (365 days in a year)
Interest = ($739.41 x 0.16 x 30) / 365
Interest = ($354.30) / 365
Interest ≈ $0.97
d. What was the unpaid balance for November after interest is charged?
To find the unpaid balance for November after interest is charged, we start with the unpaid balance before interest calculated in question a and add the interest calculated in question c.
Unpaid balance after interest = Unpaid balance before interest + Interest
Unpaid balance after interest = $630 + $0.97 = $630.97
Therefore, the unpaid balance for November after interest is charged is approximately $630.97.