Balance calculations
The Balance command uses two basic approaches to calculating a balance between payment dates. We’ll call these the proration approach and the stub-period approach.
To illustrate the differences between these two approaches, we will use the following set of sample data:
- Payments on the 15th of each month
- Balance after March 15th payment is $10,000
- Interest included in April 15th payment is $100
- Balance is needed as of March 25 (10 days after the 15th)
Prorated approach
The prorated approach starts with the balance at the last payment before the payoff date, and adds a prorated portion of interest from the next payment.
The Balance using the prorated approach would be calculated as follows:
$10,000 + (10/31) x $100 = $10,032.26
The stub-period approach computes the interest for the stub period based on the preceding Balance, the current interest rate, and the current compound period. In the above example, the interest rate is 1% per month. With monthly compounding, this means an annual rate of 12% and a daily rate of 12%/365 = 0.03288%.
The Balance using the stub-period approach would be calculated as follows:
$10,000 + $10,000 x (10 x 0.03288%) = $10,032.88
The stub-period approach is equivalent to removing all payments after the balance date and solving for a single unknown payment at that date.
How TValue does it
TValue uses the prorated approach for Rule of 78 and the stub-period approach in all other cases.
For Exact Days, Weekly, and Biweekly compounding, the results are the same with either approach. For month-based periods where the payoff date coincides with a payment date, there is no difference, since there is no fractional period.
With Rule of 78, don’t remove the payments after the balance date and solve for a single unknown payment on that date to get the balance. Rule of 78 is based on time-weighted balances considered over the entire loan. If you take out the unpaid payments, you destroy the denominator in the allocation fraction. So with Rule of 78, use the Balance command.
Note: In some cases, the interest for a fractional period is considered either earned in full or not earned at all, depending on how much of the period has elapsed. In these cases you should probably take your balance from the appropriate spot on the amortization schedule.