# Discount Calculation

### General

#### Percentage

Percentage will calculate the amount of discount by multiplying the principal portion of the payment by the original discount divided by the original principal balance.  In this case, the original principal balance was $10,000 and the original discount was$1,000.  $$\frac {1,000}{10,000} = 0.1$$, so we can compute the discount portion of the payment by multiplying the principal portion by 0.1.  We know from the previous example that the principal portion of the payment is $325.39. We can confirm this by adding the principal and discount portions in the current example. $$292.85 + 32.54 = 325.39$$. If we multiply$325.39 by 0.01 we get $32.54, the discount portion of the current payment. Percentage works differently than percentage fixed in that discount must be due on the loan in order for any of the payment to apply to it. So, in the above example, if a payment was made before the first payment actually came due on the loan, none of the payment would apply towards discount.$32.54 would then come due in discount when the payment came due.

#### Percentage Fixed

Percentage fixed works very similarly to percentage.  As you’ll notice, the discount and principal portions of the first payment are exactly the same for these two discount calculations.  The only difference is that the principal portion of a payment will always be split in the same percentage as the percent of the original discount to the total loan amount regardless of whether there is any discount due on the loan.

#### Rebalancing

Rebalancing calculates the discount as the unpaid discount divided by the remaining term of the loan.

In this case, since this is the first payment on the loan and the payment hasn’t come due yet, the unpaid discount can be calculated as the original discount of $1,000 divided by the term of the loan which is 24 months in our case. $$\frac {1,000} {24} = 41.67$$ so the discount per period will be$41.67.  This may change for future payments depending on whether the borrower pays on time or pays the full amount.  It may be that you have a short first period as well

#### Straight Line

The straight line calculation works similarly to rebalancing but the discount and principal portions are calculated once for the loan and don’t change based on payment schedule or how well the borrower repays the loan.

You’ll notice that the principal and interest portions of the first payment are exactly the same for rebalancing and straight line.  The discount portion of the straight line payments won’t change, however, except in the case of the final loan payment to make sure that all the discount gets paid and no more.