Credit Card Calculations Including Interest and Payments

Credit cards are by far one of the more complicated financial innovations in terms of personal finance. Ignoring the complexities of cash back and rewards points, as well as the benefits of a grace period on the first month’s interest, the way in which credit cards compound interest is slightly different than the way in which a normal loan or revolving line of credit would operate.

credit-cardsAs such, the equation for calculating how much time you have left on your credit card at a certain payment amount is a fairly complex beast. That being said, the underlying assumptions of the equation should be enough on its own to motivate us towards doing the math, and finding out how to get rid of these balances as soon as possible.

Credit cards differ from personal loans because of the way in which they compound interest on top of the full monthly balance that was carried, even if a payment has been made on the loan amount. This means that the amount of interest that we are paying on a credit card will always be higher than on even a comparable revolving line of credit. The addition of interest upon payments also results in a somewhat different payment schedule for the loan, as well as a period of latency between when we think we’ve paid off a card, and when we have actually paid off the card.

The end result is a completely ridiculous logarithmic equation that no person should ever need to worry about in their natural lives. Rather than waste our times with such a chore, we can use a declining balance table in a spreadsheet to look at how it is that different payment amounts and interest rates change the amount of time it would take for us to pay off a card. Firstly, we need to copy the following table into Excel:

Balance 5000 Month Principle Interest Payment Balance
Interest Rate .03 1 =B1 =E2*($B$2/12) =$B$3 =E2+F2-G2
Payment Amount 500 2 =H2+(G2*(B2/365)) =E3*($B$2/12) =$B$3 =E3+F3-G3
3 =H3+(G3*(B3/365)) =E4*($B$2/12) =$B$3 =E4+F4-G4
4 =H4+(G4*(B4/365)) =E5*($B$2/12) =$B$3 =E5+F5-G5
5 =H5+(G5*(B5/365)) =E6*($B$2/12) =$B$3 =E6+F6-G6
6 =H6+(G6*(B6/365)) =E7*($B$2/12) =$B$3 =E7+F7-G7
7 =H7+(G7*(B7/365)) =E8*($B$2/12) =$B$3 =E8+F8-G8
8 =H8+(G8*(B8/365)) =E9*($B$2/12) =$B$3 =E9+F9-G9
9 =H9+(G9*(B9/365)) =E10*($B$2/12) =$B$3 =E10+F10-G10
10 =H10+(G10*(B10/365)) =E11*($B$2/12) =$B$3 =E11+F11-G11
11 =H11+(G11*(B11/365)) =E12*($B$2/12) =$B$3 =E12+F12-G12
12 =H12+(G12*(B12/365)) =E13*($B$2/12) =$B$3 =E13+F13-G13
13 =H13+(G13*(B13/365)) =E14*($B$2/12) =$B$3 =E14+F14-G14
14 =H14+(G14*(B14/365)) =E15*($B$2/12) =$B$3 =E15+F15-G15

 

The above table shows us that we need a little more than a year to pay off a card with a $5,000 balance at a rate of 30%, making payments of $500/month. We can then manipulate the first column’s information to customize the equation to our personal financial situation. From there, we simply need to copy and paste the full table into new rows until we find that the balance reaches zero. The number of lines required will show us how many months it takes to pay off the loan.

As with other loans, it is interesting to notice just how much of a benefit there is to making large payments earlier in the loan period. In this particular circumstance, making payments of $1,000 for the first three months of the debt actually saves this borrower $251 in total interest, working out to a full 5% savings in the nominal interest rate of the loan. By manipulating this table, we can start to plan out debt calendar in a way that helps us to keep on track of our borrowings, and get the most painful of debt out of the way.

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