Nancy Tai has recently opened a revolving charge account withMasterCard. Her cre

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Nancy Tai has recently opened a revolving charge account withMasterCard. Her credit limit is $1000, but she has not charged thatmuch since opening the account. Nancy hasn't had the time to reviewher monthly statements as promptly as she should, but over theupcoming weekend, she plans to catch up on her work. In reviewing November's statement, she notices that herbeginning balance was $600 and that she made a $200 payment onNovember 10. She also charged purchases of $80 on November 5, $100on November 15, and $50 on November 30. She can't tell how muchinterest she paid in November because she spilled watercolor painton that portion of the statement. She does remember, though, seeingthe letters APR and the number 24%. Also, the back of her statementindicates that interest was charged using the average daily balancemethod including current purchases, which considers the day of acharge or credit. Assuming a 30-day period in November, calculate November'sinterest using the average daily balance method. Also, calculatethe interest Nancy would have paid with: a) the previous balancemethod, b) the adjusted balance method. Going back in time, when Nancy was just about to open heraccount, and assuming she could choose among credit sources thatoffered different monthly balance determinations, and assumingfurther that Nancy would increase her outstanding balance overtime, which credit source would you recommend? Explain.
Nancy Tai has recently opened a revolving charge account withMasterCard. Her credit limit is $1000, but she has not charged thatmuch since opening the account. Nancy hasn't had the time to reviewher monthly statements as promptly as she should, but over theupcoming weekend, she plans to catch up on her work. In reviewing November's statement, she notices that herbeginning balance was $600 and that she made a $200 payment onNovember 10. She also charged purchases of $80 on November 5, $100on November 15, and $50 on November 30. She can't tell how muchinterest she paid in November because she spilled watercolor painton that portion of the statement. She does remember, though, seeingthe letters APR and the number 24%. Also, the back of her statementindicates that interest was charged using the average daily balancemethod including current purchases, which considers the day of acharge or credit. Assuming a 30-day period in November, calculate November'sinterest using the average daily balance method. Also, calculatethe interest Nancy would have paid with: a) the previous balancemethod, b) the adjusted balance method. Going back in time, when Nancy was just about to open heraccount, and assuming she could choose among credit sources thatoffered different monthly balance determinations, and assumingfurther that Nancy would increase her outstanding balance overtime, which credit source would you recommend? Explain.

Explanation / Answer

To be able to calculate the interest under the average dailybalance method, we need to calculate the number of days eachbalance had been pending. For example, since the opening balance(on November 1st) was $600, and the first purchase (for $80) was onNovember 5th, then Nancy had a balance of $600 for 4 days. We dothe same for the next balances after the purchases and payments aremade, as per the attached excel file.

Next, in order to calculate the average balance, we use a weightedaverage using the number of days for each balance and the totalnumber of days in the month (30). For example, since the $600balance lasted 4 days, we multiply 600 by 4/30. The next balance(680) lasted 5 days, so it's multiplied by 5/30, and so on. The sumof these values is the average balance, which is found to be$584.33. Finally, we calculate the 16% interest (divided by 12,because it only accrues for 1 month and the 16% is annual) overthat amount, getting that the interest paid under the average dailybalance method is $7.79.

Under the previous balance method, interest is calculated on theclosing balance of the previous month (equal to the opening balanceof this month), which is $600. Therefore, interest is:

((16/100)/12)*600 = $8

Finally, under the adjusted balance method, which is the mostconvenient to cardholders under most circumstances, interest iscalculated over the opening balance minus any payments made in thismonth. Since the opening balance was $600 and total payments inNovember were $200, then interest is calculated over $400.Therefore, interest paid is:

((16/100)/12)*400 = $5.33

Clearly, going back in time, Nancy should have chosen a creditsource that used the adjusted balance method, as it's the one underwhich interest payments are minimum. Given that she will increaseher balance over time, it's even more convenient to use this creditsource. It should be noted, however, that sometimes interest ratesare different for these different credit sources. Therefore, theadjusted balance method is the best IF all three credit sourcescarry the same 16% APR.

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