The system provides for the possibility to apply the biweekly payment scheme. According to this scheme, the borrower repays a loan once every two weeks. Each time the payment is made on the same day of the week. A date of the first installment is calculated by the following formula: 

 First installment date= Loan origination date +14 days                                         (1)

Each successive payment is to be made in 14 days.  

The selection of a type of the payment schema (biweekly, weekly, etc.) can be best implemented as a drop-down list containing values stipulated in the agreement. The user can select a required value form a full list displayed.

A grace period is not available in the biweekly payment scheme.

Input data

In the biweekly payment scheme, the payment schedule is calculated based on the following input data:

1) Monthly interest rate (IR)

2) Loan amount (LA)

3) Loan term in months (LT) 

Calculating a number of installments

In this scheme, the loan term specified in months is transformed into a number of installments with an interval of two weeks. 

If when splitting the loan term into 14-day periods, 7 or less days remains (N <= 7), a number of periods is rounded down.

If when splitting the loan term into 14-day periods, from 8 to 13 days remains, (7 < N <=13), a number of periods is rounded up.

For example:

1) Loan term – 1 month. The current calendar month has 31 days. We obtain 2 periods spaced two weeks apart and 3 days remain. Since 3 days are less than 7, no additional period will be created.  The payment schedule must display 2 installments.

2) Loan term – 82 months. We obtain 5 periods and 12 days remain. Since remaining days fall in the range of 8 - 13 days, we create an additional period according to requirements.  The payment schedule must display 6 installments.

The number of installments is calculated by the following formula:

            (2)

where

N_inst - number of installments spaced two weeks apart,

_LTdays - loan term in days,

floor(x) - function calculating the greatest integer, the smaller integer or the integer equal to its argument x,

ceil(x) - function calculating the greatest integer, the greater integer or the integer equal to its argument x,

mod(x1, x2) - function calculating the remainder of dividing the first argument x1 by the second argument x2.

Calculating the biweekly interest rate

The monthly interest rate can be transformed into the biweekly interest rate according to the following formula:

                                                                                     (3)

where 

IR_biweekly - biweekly interest rate,

IR - monthly interest rate.

Calculating the payment schedule

The payment schedule can be created according to the classic or annuity scheme by using formulas (1)-(4) described in the articles “Classic” and “Annuity”. In these articles, a time period of one month is used as a payment period. However, in both articles, formulas (1)-(4) are invariant in relation to the measure of the payment period, i.e. values calculated by formulas (3) and (2) are to be used instead of the monthly interest rate and loan term in months.

Examples

Calculating the number of installments

Suppose that the loan was issued on November 29, 2016 for 6 months. Let us determine a number of biweekly payments.

First, we determine that 181 days are in between both dates: November 29, 2016 and May 29, 2017, i.e. LT_days = 181.

Then we determine that mod(181,14) = 13. Therefore, N_inst = ceil(181/14) = 13.

Creating the payment schedule

Let us consider the loan issued in the amount of LA = 10000 for 3 months with the monthly interest rate of IR = 0.02. The loan origination date is September 9, 2016. A grace period, grace days and commission are not available.

Monthly payments

The payment schedule generated according to the annuity scheme for regular monthly payments looks as follows: 

Biweekly payments

To create the payment schedule for biweekly payments, we determine the following values:

1. a first installment date according to formula (1)

First installment date = September 9 + 14 days + 0 days = September 23

2. a number of installments according to formula (2)

N_inst = floor(91/14) = 6, since mod(91,14) = 7 days

3. an interest rate according to formula (3)

IR_biweekly = 14 x 12 x 0.02 / 365 = 0.009205479452055

As a result, the payment schedule created according to the annuity scheme for biweekly payments looks as follows: