Repayment instalment calculations

The interest paid by the borrower to the lender is calculated on the outstanding loan amount. With each instalment there is a small amount of the loan principal repaid and this reduces the interest charge for the next month. Because each monthly payment remains same, the amount of principal that is repaid will increase slightly each month and the interest will reduce. As the loan principal is repaid to the lender it is available to lend out again.
For users of Microsoft Excel there are some functions that can calculate monthly repayment and the amount of capital repaid and interest paid.
Taking a £10 loan at 7% over 36 months as an example.

The Excel function PMT provides the monthly repayment = PMT (rate, nper, pv, fv, type)
where
rate = nominal interest rate of the loan
nper = number of repayments
pv = present value or principal of the laon
fv = is optional. It is the future value or the loan amount outstanding after all payments have been made. If this parameter is omitted, the PMT function assumes a value of 0.
type =is optional. Repayments are due at the end of the period (0) or repayments are due at the beginning of the period (1). If this parameter is omitted, the PMT function assumes a value of 0.

Eg= PMT( (1+7%)^(1/12)-1 , 36, -10, 0, 0 )= £0.3078( outstanding amount) * ((1 + rate%) ^ (days/365.25)-1) 

There are two Excel functions that provide the capital repayment and interest that is due for a specific period. These are:
Capital = PPMT( rate, per, nper, pv, fv, type )
Interest = IPMT ( rate, per, nper, pv, fv, type )

For the 3rd payment, the capital and interest payment breakdown is as follows
Capital: PPMT( (1+7%)^(1/12)-1, 3, 36, -10, 0, 0 ) = £0.2541
Interest: IPMT ( (1+7%)^(1/12)-1, 3, 36, -10, 0, 0 ) = £0.0537
The table below shows some repayments:

Notwithstanding the above, adjustments will be made for the following: -
1) The borrower has the choice of the date of the first repayment, which may be no earlier than 15 days, and no later than 42 days, from loan acceptance. The amount of principal and interest paid/received on the first repayment is adjusted to this period of the loan. The additional interest from the period between the first repayment and the second is also added to the first repayment. The first repayment will therefore be a different amount to all the subsequent repayments.
2) The second and subsequent repayments will all be the same amount and payable on the same date of each month. However, the borrower has the choice of the day of the month on which these repayments are made, but no earlier than 10 days and no later than 33 days, after the first repayment. We feel that this is a good compromise providing the borrower with the flexibility to choose dates that will work regarding salary payments, etc., but without the lender receiving the first two repayments with too little or too much time between them.
3) Fractions of pence are not possible therefore the repayment amount might vary slightly from month to month to take into account the fractions.
4) Borrowers may choose to change their repayment schedule in a number of ways. For this they have to buy a Change in Instalment Plan membership. This endeavours to compensate the lenders for changing their lending.