If a loan is set up using one of the Rule of 78s interest methods, the posting of the accrual to the general ledger can either be done normally (in this case by the rule of 78 where the posting of income matches the interest accrual) or by the actuarial method. The Rule of 78 accelerates the accrual of interest at the start of the loan, and the purpose of using the actuarial method for posting to income is to avoid having that acceleration reflected in the ledger. The difference between the amount of interest accrued (by the Rule of 78) and the amount of interest reported (by the actuarial method) will reach a maximum at approximately the mid-point of the loan, then will reduce until the two become equal at the point of the loan’s maturity. If there is an early payoff on the loan, a transaction will post the outstanding difference to income.

The actual posting of the interest to the ledger may be accomplished by either the Accrual Basis or the Cash Basis accounting method.

The following is an example showing mathematically, the difference between a Rule of 78 accrual and an actuarial Accrual:

A loan is added with the following settings -

• Interest Method - Rule of 78 (simple)
• Use Actuarial Interest
• Principal - $10,000
• Interest Rate - 10%
• Term - 5 years (60 months)

In addition, for the purposes of this calculation, assume that the first month of the loan is a 30 day month (e.g. April, June, September, or November)

The pre-computed interest for a $10,000 loan, amortized over 60 months at 10% is: $2,748.19 (this may be derived from the amortization schedule of a simple interest loan entered into the system).

The summation of the numbers 1–60 is 61 x 30 = 1,830

The amount of interest per 1 is $2,748.19/1,830 = $1.50174

For the first period of the loan, the number to be used is the total number of payments, so the interest to be accrued and paid the first month will be $1.50174 x 60 = $90.10440.

The daily interest accrued in a 30 day month is $90.10440/30 = $3.00348 (this is the per diem interest for the Rule of 78).

Now, for the purpose of posting income to the ledger, the per diem is again calculated by the actuarial method -

$10,000 x 10% = $1,000 (annual interest)

$1,000 / 12 = $83.33333 (periodic interest)

$83.33333 / 30 = $2.77778 (Actuarial per diem)

So, this loan accrues $3.00 of interest per day for the purpose of calculating the borrowers payment, but only posts $2.78 to income in the general ledger. The difference of $0.22 is posted to a deferred interest income account.

When a Rule of 78 loan is set for Actuarial Accounting, extra transactions are created for controlling the posting of the interest to the General Ledger.

This example, which uses the figures from the previous example, will go through each of the transactions that occurs and show how they affect the ledger, as well as any changes that are required to the setup in order to facilitate the use of this method.

First, when a loan of this type is added to the system, in addition to the Principal Advance transaction, a transaction will be automatically posted to realize the amount of the pre-computed interest up-front . In our example loan, the two transactions are as follows:

Transaction Code	Transaction Description	Transaction Amount	Debit Account	Credit Account
100	Principal Advance	10,000	Loan Asset1	Cash Account1
110	Pre-computed Interest	2,748.19	Loan Asset1	Accrued Deferred Interest1

The Ledger balances associated with this loan, after these transactions are as follows:

General Ledger Account	Debit Balance	Credit Balance
Loan Asset1	12,748.19
Cash Account1		10,000
Accrued Deferred Interest1		2,748.19

On a daily basis, interest accrues. Two accrual entries are made each day: the Rule of 78 interest and the Actuarial Interest. The entries are posted to the Ledger in the following manner:

Accrual Type	Accrual Amount	Debit Account	Credit Account
Rule of 78 Accrual	3.00348	Accrued Deferred Interest1	Deferred Interest Income1
Actuarial Accrual	2.77778	Deferred Interest Income1	Interest Income1

After 30 days of accruals, the balances of the Ledger Accounts are as follows:

General Ledger Account	Debit Balance	Credit Balance
Loan Asset1	12,748.19
Cash Account1		10,000
Accrued Deferred Interest1		2,658.08560
Deferred Interest Income1		6.77100
Interest Income1		83.33340

Now the interest balance of $90.10 is paid. In addition to the standard interest payment transaction, a transaction will be automatically run by the system (TC 214) for the payment (on the Ledger) of the Actuarial Interest. By default, this transaction code is set with no General Ledger entries. If you are using this kind of accounting, you should set this transaction to debit the Accrued Interest1 (to offset the credit of the interest payment) and to credit Loan Asset1. If you configure the transaction code in this way, the interest payment transactions will look like this:

Transaction Code	Transaction Description	Transaction Amount	Debit Account	Credit Account
202	Interest Payment	90.10	Cash Account1	Accrued Interest1
214	Rule of 78 Actuarial Payment	83.33	Accrued Interest1	Loan Asset1

The final Ledger balances after the interest payment are as follows:

General Ledger Account	Debit Balance	Credit Balance
Loan Asset1	12,664.86
Cash Account1		9,909.90
Accrued Deferred Interest1		2,658.08560
Deferred Interest Income1		6.77100
Interest Income1		83.33340
Accrued Interest1		6.77100

The balance in Deferred Interest Income1 represents the difference between the interest that has been accrued and the interest that has been applied to the ledger as Income.

The balance in Accrued Interest1 represents the difference between the interest that has been paid and the interest payment that has been applied against the Loan Asset. These balances will generally coincide. They will build to a maximum by approximately the midpoint of the loan and will then decrease. They will be zero (i.e. the interest accrued and taken as income will be equal, and the Interest paid and applied to the asset will be equal) by the final payment of the loan upon maturity. If the loan is paid off early, settlement transactions will post the additional interest to the income and charge the credit balance in Accrued Interest against the asset.

In order to run the ledger by Cash Basis when using Actuarial Accounting on Rule of 78 loans, you will need to make the following modifications to the default setup:

1. Make sure that the Loan Group Setup has the following place-holders all set to NONE: Accrued Deferred Interest1, Deferred Interest Income1, and Interest Income1. Each of these place-holders will be hit with a general ledger entry during the nightly accrual process, and you do not want your nightly accruals to go to the GL when you are doing cash basis accounting.
2. Set up custom GL place-holders for CB Deferred Interest and CB Interest Income, and map these in the Loan Group to the GL accounts where you will hold the unpaid deferred income and the interest income accounts respectively.
3. Modify transaction code 110 so that it credits the CB Deferred Interest (instead of Accrued Deferred Interest1).
4. Modify all Interest Payment Transaction Codes (202, 206, 210, and 222) so that they credit the Loan Asset1 (instead of the Accrued Interest1).
5. Modify transaction code 214 so that it debits CB Deferred Interest and credits CB Interest Income.

When you add the loan, the full amount of the principal and the expected interest will debit the loan asset. The principal will credit cash, and the amount of the expected interest will credit the Cash Basis Deferred Interest.

During the nightly accrual process, no General Ledger entries associated with interest accruals will reach any GL accounts.

When an interest payment is made, the amount of the interest payment will credit the loan asset (debit is to cash). An additional transaction will automatically be generated for the actuarial amount of the interest paid (trans code 214). This actuarial amount will debit the Cash Basis Deferred Interest and credit the Cash Basis Interest Income.