I'm currently testing this Loan Amortization Software. I can enter in a Principal amount, Interest, Payment durations and future value in the end of the duration, When payments are to be made, Beginning or the End. And it'll give me a "payment amount". I'm wondering Why does the payments different if you select Beginning and "end". Would it matter if you select 15th ? If so what formula is involved to calculate payments?
Imagine you owe somebody $1000 and you will make 12 monthly payments with 6% interest (1/2 or a percent per month).
If the balance accrues interest before the first payment is made, you will owe $1000 + $5 when you send in the first payment. That extra $5 is 1/2 % of 1000. That will mean you have to make a monthly payment of ~$86.07.
If you don't accrue interest before the first payment is made you will only need $85.64 each month to pay off the loan.
Your software has to decide how much interest has accrued before applying the first and subsequent payments. If you want 15 days of interest to be included then adjust your balances accordingly.
What you are describing sounds like a financial calculator -
The first piece of electronics I ever loved was a TI BA35 (image here). The calculations for time value of money are all described by these 5 variables, Number of periods, interest per period, Present Value, Payment, and Future Value.
The beginning/end issue arises depending on whether you're adding money, as in deposits on the first of each month with interest accruing, or payments as with a mortgage, made at month end. The mortgage typically starts on the first of the month, with the payment due on the first day of month 2.