Interest Calculation Methods in Loans
• 26 Oct 2020
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# Interest Calculation Methods in Loans

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## Overview

The interest on loans is accrued on a daily basis, which allows you to charge your clients only for the days they actually used the loan amount.

So, for instance, if a client pays back before the due date, Mambu will display the exact interest amount that the client owes at that moment. Also, when a repayment is late, interest will keep being accumulated each day.

The only calculation method in which interest is not accrued in Mambu is Fixed Flat. When using this method, the interest always reflects the amount that would be due on the due date, regardless of the actual payment date.

The Interest Rate Source allows organizations to fix their interest rate to a standard – the index – which is determined externally.
The Days in Year setting will determine how interest will be accrued.

## Interest Calculation Methods

There are three different interest calculation methods you can choose from for your loan product:

• Flat
• Declining Balance
• Declining Balance with Equal Installments

When creating a new loan product, you need to choose one of these methods to be associated with that product and all the accounts created under it.

Click to see where to set the Interest Calculation Method method for loan products. Next you can see how the repayment schedules would look for each of the methods.

The loan details for every example are:

• Amount: 1000
• 4 installments
• Repayments are made every: 1 Month
• Interest Rate: 10%
• Interest Rate Frequency: Monthly
• Disbursement Date: 1/23/2011
• 365 days

### Fixed Flat

This is the only method for which interest is not accrued over time. All interest and principal become due immediately upon disbursement and regardless of the first repayment date.

The interest due depends only on the interest rate, principal amount and time between repayments. ### Declining Balance

The Declining Balance method reflect the actual cost of the loan more accurately than the Flat method, as the interest is calculated on the outstanding balance.

The client only pays interest on the actual amount they still owe and not on the total amount (as is the case with the Flat method).

In this case, as the client starts making repayments, the interest due keeps decreasing over the duration of the loan. ### Declining Balance (Equal Installments)

Just like for the Declining Balance method, the interest is calculated on the outstanding principal amount. The difference for the Declining Balance (Equal Installments) method is that the client pays equal installments for the duration of the loan. This is achieved by increasing the amount of principal being repayed as the interest decreases, adding up to the same fixed amount for each installment. #### Non-equal installments due to rounding and first repayment date

In some situations, it can happen that one of the installments is different than the others.

This can occur, for instance, when the time from disbursement until the first repayment date is longer than the time between each installment. In this case, there will be more interest accrued and less principal in the first installment, and the remaining principal is added to the last or to the first installment – as defined in the loan product settings.

Click to see where to set the Rounding of Repayment Schedules option for loan products. ## Interest Type

For Dynamic Term Loans, you can choose between two Interest Types for loan products:

• Simple Interest
• Capitalized Interest
Click to see where to set the Interest Type for Dynamic Term loan products. ### Simple Interest

Simple Interest type is the default interest type for for Dynamic Term Loans with both the Declining Balance and the Declining Balance Equal Installments Interest Calculation Methods.

For the Declining Balance method, simple interest is determined by simply multiplying the daily interest rate by the principal, and then by the number of days that elapse between payments.

For the Declining Balance (Equal Installments) method, Simple Interest can be calculated in 2 ways:

• Principal Only – the default option, which calculates interest by simply multiplying the daily interest rate by the principal and then by the number of days that elapse between payments.
• Principal and Interest – new option, which calculates the interest by multiplying the daily interest rate by the principal and unpaid interest and then by the number of days that elapse between payments.
Click to see where to set the Calculate Interest Using option for Declining Balance (Equal Installments) | Simple Interest loan products. Example of Principal and Interest calculation:
Consider a loan with the following terms:

• Loan amount: \$1000
• Interest Rate: 10% per year
• No of installments: 5
• Monthly Repayments
• Disbursement date: 01.01.2020
• Total Due (PMT): 205.03
• Days in Year method: 30E/360

Step 1:
On the first installment due date (01.02.2020), calculate the interest based on Principal and Interest:

Interest amount = IR*(Principal Balance + Interest Balance)*no_of_days/360
= 10*(1000+0)* 30/360 = 8.33

If we apply the interest, Interest Balance will be 8.33.

Step 2:
On the second installment due date (01.03.2020), calculate the interest based on Principal and Interest:

Interest amount = IR*(Principal Balance + Interest Balance)\no_of_days/360
= 10%*(1000+8.33)*30/360 = 8.40

If we apply the interest, the Interest Balance will be 8.33 (interest applied on the first installment) + 8.40 (interest applied on the second installment) = 16.73

The interest is updated in the schedule with the new calculation based on Principal and Interest after it is applied.

If the repayments are paid on time, Interest Balance will always be 0, and this method will act exactly like the Principal Only Interest Calculation Method.

### Capitalized Interest

The Capitalized Interest type is available for Dynamic Term loans with both Interest Calculation Methods (Declining Balance and Declining Balance (Equal Installments)).

Click to see where to set the Interest Calculation Method method for loan products. When this type of interest is used for Declining Balance loans, the interest amount is capitalized into the principal balance and increased from one installment to another. In the schedule, the principal amount is allocated on the last installment, previous installments having only the interest capitalized. For Dynamic Term loans with the Interest Calculation Method Declining Balance (Equal Installments), the interest amount is capitalized into the principal balance like for Declining Balance loans, the only difference being that Declining Balance (Equal Installments) loans have principal and interest on each installment.

## Accrue Late Interest

Normally, businesses have a legal right to charge interest on late payments. However, you may want to disable this option; for example, if you want to create a flexbile product which rewards customers for paying on time rather than penalises them for paying late.

The Accrue Late Interest option is available for Dynamic Term loan products using the Declining Balance (Equal Installments) Interest Calculation Method and the On Upcoming Pending Installment Only Pre-Payment Allocation method. Within this group of products, the Accrue Late Interest option is available for both Pre-Payment Recalculation methods (Reduce Amount per Installment and Reduce Number of Installments). The feature is available for all Payments Methods (Standard, Balloon and Optimized).

The feature is available via API 2.0 and the UI.

To uncover the Accrue Late Interest checkbox in the UI, follow these steps (click to expand):

Under Product Type , select Dynamic Term Loan. In the Interest Rate section, set the Interest Calculation Method to Declining Balance (Equal Installments). In the Repayment Scheduling section, ensure that the Payments Method is set to Standard Payments. In the Repayment Collection section, set the Pre-Payment Allocation method to On Upcoming Pending Installment Only. This uncovers the options for Pre-Payment Recalculation methods in the same section. Set the Pre-Payment Recalculation method to Reduce Number of Installments. This uncovers the Accrue Late Interest checkbox in the Interest Rate section. Even though the Accrue Late Interest option is available for Declining Balance (Equal Installments) loans with the Pre-Payment Recalculation Method Reduce Amount per Installment, the Accrue Late Interest checkbox only appears if the Pre-Payment Recalculation method is first set to Reduce Number of Installments (and Payments Method is kept Standard).

Mambu is working on changing this for future releases. In the meantime, please follow the steps above to uncover the Accrue Late Interest checkbox, then change the Pre-Payment Recalculation method or the Payments Method if necessary.

Accrue Late Interest is enabled by default for loan products. You can uncheck this box in order not to accrue and apply late interest for issued loans. ## Interest Rate Source (Fixed or Indexed)

In Mambu you can set up two types of interest rate sources, via the Interest Rate Source setting of the loan product:

• Fixed
A fixed interest rate, which is used for the the entire lifetime of the loan.
• Indexed
The interest rate is fixed to a standard rate which is determined by an external entity, such as a government. In this case loans will need to be updated to reflect the new interest rate whenever it changes.
Click to see where to set the Index Rate Source option for loan products. Index rates are defined under Administration | General Settings | Rates and can only be applied to non-Flat Interest Calculation Methods, since, for Fixed term with Flat Interest calculation products, the interest amounts are fixed from the beginning and can not change.

The frequency at which the interest rate should be reviewed is determined when creating a product and can be set on a daily, weekly or monthly basis. If there is a new rate when the review is made, then all loans using that source as an Index Interest Rate will be updated.

The installment immediately following the review does not change, only subsequent installments do.

Example
Consider a loan with the following terms:

• Loan Amount:\$1000
• Interest:5% (index) + 2% (Spread)
• Monthly Installments
• Disbursal date: 13.12.2011
• Interest Frequency Review: Monthly

Now suppose that on January 1, the Central Bank keeps the Index rate to 5% and on February 1 increases it to 6%.
The change will affect the loan's repayment schedule, according to the frequency review (in this case, the interest rate will be changed starting with 13.02.2012, 1 month from activation):

• First installment on 13.01.2012 – Interest: 7% (5% Index + 2% Spread) and total due will not be changed
• Second Installment on 13.02.2012 – Interest: 7% (5% Index + 2% Spread) and total due will not be changed
• Third Installment on 13.03.2012 – Interest: 8% (6% Index + 2% Spread) and total due will be changed (in case of equal installments, a new PMT will be generated, based on the new interest rate)
• all the following installments will use the Interest: 8% (6% Index + 2% Spread) and will have the total due changed

Index Rate Constraints
You can apply a floor (min) or ceiling (max) to index interest rates as well. That is, that the combined index + spread cannot be less than or more than a predefined value. These limitations can be defined as part of the loan product configuration, and they will apply to all accounts based on this loan product. In addition, you can set a default for the interest rate.

Click to see where to set the Interest Rate Default, Floor and Ceiling for loan products. Example
Assume floor rate = 10% and ceiling rate = 20%

Index Interest Rate Spread Actual Rate
10 5 15
10 17 20
5 3 10

## Days in Year

You can choose from three different ways to accrue interest on a loan:

• Actual 365/Fixed – calculates the interest daily by counting the number of days in the calendar and uses a fixed 365 year length.
• Actual/360 – also computes the interest daily by counting the number of days in the calendar, but uses a fixed 360 year length.
• 30E/360 – counts the days from the calendar, but also introduces some changes on the months with 31 and 28 days.
Click to see where to set the Days in Year option for loan products. Particulars of the 30E/360 method
When using this method, months that have 31 days will be considered to have 30 days. This implies that the number of accrued interest days will be the same on the 31st of that month as on the 30th.

The last day of February is treated as the 30th day of the month.

Furthermore, the 30E/360 days in year method will compute the interest knowing that there is a maximum of 360 interest days in that year. So for instance, if a loan account has repayments paid yearly, the interest will be calculated for 360 days, instead of the actual number of days in the calendar.