# Interest Application

### Introduction

Interest application lets you choose how interest accrues. Most LMS users will choose to base that accrual on transactions, but it can also be based on payment periods. These options will not affect the original payment schedule, but they do determine how much interest will come due when a payment applies and the date payments apply to the loan.

When you log a payment, you will see different options for extra towards, depending on your interest application. See the Extra Towards Mapping article to understand how changing this setting can change your payment application.

### Between Transactions

In the between transactions scenario, payments will apply to interest that accrues on the loan daily. Interest will not show up as part of the amount past due on the loan unless the scheduled payment that should have covered that interest has passed without being paid.

Here is an example of how a payment will apply in a between transactions scenario:

As you can see, the first payment on this loan came due on 10/01/2015. The payment wasn’t actually made until 10/10/2015. In the scheduled payment, the interest is $205.48. In the actual payment$267.12 applied towards interest. The reason for the additional interest accrual is the extra days that passed between the due date and the date the payment was actually made.

So, how is the interest calculated in this situation? This is a $10,000 loan with a 25% interest rate and a term of 24 months. Due interest is calculated as: Due Interest = Daily Interest Rate * Outstanding Principal Balance * Number Of Days Since The Last Payment We'll first need to calculate the daily interest rate. Divide the yearly interest rate by the number of days in a year. This loan is using the actual number of days in a year. As an equation, that looks like this: $$\frac{YearlyInterestRate}{365} = Daily Interest Rate$$ Here it is with the numbers from our example (note that 25% become .25): $$\frac{\text{.25}}{365} = 0.000685$$ Now that we have the daily interest rate, we can plug it back into our due interest formula and calculate the interest that should be paid by the payment on 10/10, which is 39 days since the contract date. $$0.000685 \ast 10,000 \ast 39 = 267.12$$ ### Between Periods In a Between Periods scenario, interest comes due by period. When a payment is made, it covers the interest for the current period, or the previous period, if the payment is made late. Payments that are made late impact the average daily balance for the next period, so interest in the subsequent payment period will be higher. Let’s first calculate the interest for the payment that was made on 10/10. We can do this by multiplying the daily interest rate by the average daily balance and the number of days in the period. First we will compute the daily interest rate. $$\frac{25%}{365} = 0.0685$$ Now we will compute the first period interest. Here's the formula we'll use: Daily Interest Rate * Average Daily Balance * Days In Period = First Period Interest And here's the equation with our own variables plugged in (converting our interest rate into a decimal): $$0.000685 \ast 10,000 \ast 30 = 205.48$$ Now we will compute the interest portion as shown in Forecasted Payment: 2. The daily interest rate will be the same (0.0685%) so we will start by computing the new average daily balance. We compute the daily average balance by adding together the balance at every day of the period, then dividing by the number of days in the period. $$Average Daily Balance = \frac{b_{1} + b_{2} + \cdots + b_{n}}{n}$$ • b = balance on a given day • n = number of days in a period Figuring out the balance on each day is actually a little easier than it sounds. There are only two balances: before and after the payment is applied. Just multiply the balance before payment by the number days before payment, and the balance after by the number of days after. $$Average Daily Balance = \frac{(b_{1} \ast d_{1}) + (b_{2} \ast d_{2}) }{n}$$ • b = balances. b₁ is the balance before payment; b₂ is the balance after. • d = number of days. d₁ is the number of days before payment; d₂ is the number after. • n = total number of days in the period. This should be equal to the sum of d₁ and d₂. Here's that equation with our variables plugged in: $$\frac{(10,000 \ast 9) + (9,671.76 \ast 22)}{31} = 9,767.06$$$9,767.06, then, is our Average Daily Balance, which we can use to calculate First Period Interest.

Math Breakdown

Here's a breakdown of each step in that equation.

$10,000 (principal balance at the beginning of the period) x 9 (days in the period before the payment applied) = 90,000$9,671.76 (principal balance at the end of the period) x 22 (days in the period after the payment applied) = 212,778.72

90,000 (daily total for first 9 days) + 212778.72 (daily total for last 22 days of the period) = 302,778.72 total of daily balances for the period

302778.72 (total of daily balances for the period) / 31 (days in the period) = \$9767.06 (average daily balance for the period)

Now we can compute the interest for the period. You might recall the formula:

Daily Interest Rate * Average Daily Balance * Days In Period = First Period Interest

With our own values plugged in, we get this:

$$0.000685 \ast 9,767.06 \ast 31 =207.38$$

You can give the borrower the benefit of an early payment by choosing Yes from the Early Payment drop-down when you log the payment. Choosing Yes for this option will do an average daily balance adjustment in the period when the payment is made, causing less interest to accrue.