Understanding the Mathematics of Personal Finance

SOME CALCULATION EXAMPLES

For the following examples, I’m going to start each month (which will have 30 days and will also be the billing period) with the same initial situation: [17]

EXAMPLE 6.1 Table 6.2

I pay my bill in full ($821.08) and vow to never use my credit card again. As you can see from the table, my balances just come forward day after day until day 12. Since I have sent in the full payment, everything gets zeroed out and my daily balances are 0 from the twelfth day until the end of the month.

At the end of the month, the bank again calculates the ADB. This is a simple calculation—in each category, add up all the daily balances and then divide this number by the number of days in the month. Shown in the table are the purchase ADB of $123.77 and the cash advance ADB of $177.29.

These ADBs in turn create interest payments of $1.12 and $3.35 for the purchase and cash advance ADBs, which in turn add up to a total new balance of $4.47. This amount is billed. It takes 2 months of paying bills fully to clear my account. This will be relevant when I discuss grace periods below.

EXAMPLE 6.2 TabU 6.3

This example is the same as the previous example except that I didn’t have the cash on hand to fully pay my bill. Instead, I paid $300.

The credit card company first applies a payment to the lowest interest-bearing balance in the account, in this case, the purchase balance. Since the purchase balance of $337.54 is higher than the payment of $300, the purchase balance absorbs the entire payment.

For the rest of the month, the daily purchase balance is $37.54, and the cash advance balance is $483.54.

At the end of the month, the ADBs are calculated as before, as are the month’s finance charges. I end the month owing $38.89 on my purchase balance and $492.98 on my cash advance balance. My monthly statement shows a total due of $531.86.

If these balances were being carried on two different credit cards, I could have optimized things a bit. Rather than paying $300 to the purchase balance, I would have paid the minimum payment required to the purchase balance, and then paid the remainder of my $300 to the cash advance balance. Since the cash advance balance accrues such a high interest rate in this example, the annoyance of writing two checks and the cost of the extra postage stamp would have been well worth the effort. I should of course watch out for incurring a minimum finance charge.

EXAMPLE 6.3 TabU 6.4

This example extends the previous examples to show a fairly busy month. There are three purchases, two cash advances, and one payment. In this example, I made the payment larger than the purchase daily balance, so the purchase daily balance is fully paid off and some of the payment gets applied to the cash advance daily balance.

Notice the trend as time progresses for the cash advance balance, the balance that accrues interest at a very high rate. This slowly becomes the dominant part of the total balance. [18]

Day

Item

Purchases

Advances Credits ($)

Purchase daily balance ($)

Advance daily balance ($)

1

337.54

483.54

2

337.54

483.54

3

337.54

483.54

4

337.54

483.54

5

337.54

483.54

6

337.54

483.54

7

337.54

483.54

8

337.54

483.54

9

337.54

483.54

10

337.54

483.54

11

337.54

483.54

12

Pmt

821.08

0.00

0.00

13

0.00

0.00

14

0.00

0.00

15

0.00

0.00

15

0.00

0.00

16

0.00

0.00

17

0.00

0.00

18

0.00

0.00

19

0.00

0.00

20

0.00

0.00

21

0.00

0.00

22

0.00

0.00

23

0.00

0.00

24

0.00

0.00

25

0.00

0.00

26

0.00

0.00

27

0.00

0.00

28

0.00

0.00

29

0.00

0.00

30

0.00

0.00

ADB:

123.77

177.29

Interest:

1.12

3.35

Balance due:

1.12

3.35

Total due:

$4.47

Day

Item Purchases

Advances Credits ($)

Purchase daily balance ($)

Advance daily balance ($)

1

337.54

483.54

2

337.54

483.54

3

337.54

483.54

4

337.54

483.54

5

337.54

483.54

6

337.54

483.54

7

337.54

483.54

8

337.54

483.54

9

337.54

483.54

10

337.54

483.54

11

337.54

483.54

12

Pmt

300.00

37.54

483.54

13

37.54

483.54

14

37.54

483.54

15

37.54

483.54

15

37.54

483.54

16

37.54

483.54

17

37.54

483.54

18

37.54

483.54

19

37.54

483.54

20

37.54

483.54

21

37.54

483.54

22

37.54

483.54

23

37.54

483.54

24

37.54

483.54

25

37.54

483.54

26

37.54

483.54

27

37.54

483.54

28

37.54

483.54

29

37.54

483.54

30

37.54

483.54

ADB:

148.79

499.65

Interest:

1.34

9.44

Balance due:

38.89

492.98

Total due: $531.86

Day

Item

Purchases

($)

Advances

($)

Credits ($)

Purchase daily balance ($)

Advance daily balance ($)

1

337.54

483.54

2

337.54

483.54

3

337.54

483.54

4

337.54

483.54

5

Purchase

150.00

487.54

483.54

6

487.54

483.54

7

487.54

483.54

8

Advance

100.00

487.54

583.54

9

487.54

583.54

10

487.54

583.54

11

487.54

583.54

12

Pmt

500.00

0.00

571.08

13

0.00

571.08

14

0.00

571.08

15

0.00

571.08

15

Advance

100.00

0.00

671.08

16

0.00

671.08

17

0.00

671.08

18

0.00

671.08

19

0.00

671.08

20

Purchase

75.00

75.00

671.08

21

75.00

671.08

22

75.00

671.08

23

75.00

671.08

24

Purchase

5.80

80.80

671.08

25

80.80

671.08

26

80.80

671.08

27

80.80

671.08

28

80.80

671.08

29

80.80

671.08

30

80.80

671.08

ADB:

187.62

624.68

Interest:

1.69

11.80

Balance due:

82.50

682.88

Total due:

$765.38

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