Chapter 24
Personal Money Computations

3  Credit and Debt Accounts (II)

Suppose you have an account with a business (bank, firm, insurance company, etc). Assume all your payments to the business are recorded as credits. Further assume all the payments from the firm to you are recorded as debts or debits. The business may be content to continuing dealing with you if the value of credits is greater than the value of your debts, or if you have an arrangement to pay your debts in regular fashion. For the calculations that follow, we assume that a dollar credit grows with compound interest precisely at the same rate as dollar of debt. Otherwise, the following calculations and the conclusions drawn from them will be false.

The difference between the accumulating total credit and the accumulating total debt or debits gives what is owed by you to or by you to the business in question. Now if you withdraw a dollar from the firm and then immediately return it, there is an extra dollar of debt and also an extra dollar of credit recorded. The difference does not immediately change. Moreover, because the extra dollar of debt grows at the same rate as the extra dollar of credit, the future difference is not changed by the simultaneous addition of a dollar debt and a dollar credit. This implies we can add or subtract the same amount from credit and debt record, or changing the difference now and in the future because they both grow or compound at the same interest rate.¹ Only the difference matters.

Because of this when you make a payment to the business in question you have the option of recording it as an credit and then subtracting the same amount from both the credit and debt balance. The latter is equivalent to subtracting the payment from the outstanding debt and leaving the credit balance unchanged. This implies choice or flexibility in tracking the amount owed to or by you. Three options are described.

 

1. Record all the credits and debits, and how they accumulate and compound, separately. The difference gives your account balance. This was the option described above. This is the two-account method used in the previous section.
2. Record the credit and debits together in a single account. This single account balance will equal the previous difference (provided the interest rate here is always the same as that for the credits and debits recorded separately.)
3. Mix the previous two approaches as convenient in your calculations of the difference: That is, you may use some payments to the business to either increase your credit balance or lessen your debt balance; and use payments from the business to reduce your credit balance or increase in your debt balance.

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