MathDBase Project's video: Personal Finance Math 3: Calculating Credit Card Finance Charges Part 2

Personal Finance Math 3: Calculating Credit Card Finance Charges, Part 2: By the average daily balance method How to reconcile results found on your credit card statements. In this anicast we calculate credit card finance charges and new balances using the average daily balance method. Though periodic finance charges are always calculated using the same formula, the balance that is subject to finance charges is calculated using a variety of methods. In this series, we will cover three of those methods: the Average Daily Balance Method, the Previous Balance Method and the Adjusted Balance Method. We will discuss the average daily balance method in this anicast. The average daily balance is calculated by finding the sum of the balances at the end of each day in a billing cycle, then dividing by the number of days in the cycle. The periodic finance charge is then figured by multiplying the periodic rate, daily or monthly, by that average daily balance and the number of periods. There are two kinds of average daily balance, one that includes new purchases and one that does not. To calculate finance charges using the average daily balance including new purchases, we can use the following formulas The daily balance including new purchases is equal to the beginning balance minus payments and credits plus purchases and fees. The new balance is equal to the previous balance plus finance charges, new purchases and fees minus payments and credits. As an example, suppose Mrs. Winters’ credit card statement showed the following transactions for March of 2014: 3/1 Previous balance: $7,312; 3/5 Purchase: $289.12; 3/16 Purchase: $27.26; 3/20 Payment: $315.00; 3/22 Purchase: $4.19. Her card uses the average daily balance method, a monthly periodic rate with an APR of 17.2%. Calculate the finance charge and new balance. First, let’s organize the transactions in a table. …The date column is self-explanatory. In the transactions column, purchases are added because they increase the amount that is owed and payments are subtracted because they decrease the amount that is owed. The balance column reflects the changes in the outstanding balance on the card after purchases and payments. The number of days column indicates how many days a balance amount has remained unchanged. And each entry in the sum of daily balances column is the product of the specific static balances and the number of days they remained unchanged…which is the same as adding those balances to each other the number of times indicated in the number of days column. The last entry in this column, is the sum of all entries above it. Now, divide the total from the sum of daily balances column by 31, the number of days in the billing cycle, to find the average daily balance, which is $231,176.30 divided by 31 or $7,457.30. The monthly periodic rate is 17.2% divided by 12 or 0.172 divided by 12, which is 0.014333. And the finance charge is the product of the average daily balance and the monthly periodic rate, or $7,457.30 times 0.014333, which is $106.89, rounded to the nearest penny. The new balance is equal to the previous balance plus finance charges, new purchases and fees minus payments and credits, so we have $7,312 plus $106.89 plus $289.12 plus $27.26 plus $4.19 minus $315, for a new balance of $7,424.46. The calculation of the finance charge if new purchases are excluded is similar to what we just did, it just doesn’t include any of the new purchases during the billing cycle. To calculate Mrs. Winters’ finance charge and new balance if new purchases are excluded, we’ll start again with a table similar to what we used earlier, but this time, the only transaction was the payment on March 20th. Since there are now only two entries, the number of days for the static balances will also have to change to reflect that. Now, the average daily balance is $222,892 divided by 31 or $7,190.06, rounded to the nearest penny. The monthly periodic rate is the same as before, so the finance charge in this case is $7,190.06 times 0.014333 or $103.06, rounded to the nearest penny. The new balance is calculated exactly as we did before, the only difference is the lower finance charge. So we have $7,312 plus $103.06 plus $289.12 plus $27.26 plus $4.19 minus $315.for a new balance of $7,420.63. Credit cards using the average daily balance excluding new purchases will generally have a lower finance charge.