Rule of 78 Actuarial Interest Accounting
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.
NoteFor this loan type, there will always be a GL posting for both the amount of the Actuarial accrual and the rule of 78 accrual. The setup of your loan group and transaction codes will control to which GL accounts each accrual posts and how the difference is resolved upon payoff of the loan.
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.