# Why Do We Round-Up (Day 198)

Finally realized why in some cases we need to round-up the numbers--when setting up a payment plan, applying the usual rounding logic sometimes may increase a month.

Let's look at an example: a \$100 payment splits into 12 "equal" installments with no interest. If we round the monthly payment, from \$8.3333333333 to \$8.33, after 12 months, the total payment is only at \$99.96, so there needs to be a 13th month payment of \$0.04 to add up the numbers.

So if we always round-up, the monthly payment will be \$8.34 instead. And \$8.34 x 12 = \$100.08. So the user pays \$8.34 for 11 months, then for the last month, the user pays 8 pennies less--\$8.26. This matches the term correctly.

However, if we accept extra payments in between, there still may be cases where the last month payment ends up being \$1.00 or less...

What is the usual way of handling this? What is the typical threshold when we decide to roll up the residual payment into the current one? Need some help from the accountants. ^_^

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