In our bank, the management decided to change the exsiting method of loan calculation from the normal reducing to the CRA method which is calculating the installment through the pmt function pmt= (rate/12,period,principle)in the excell

during the new system testing i entered a loan which contains a grace period so the client will not pay for 1 month for example:

principle 1000, 10 months repayment, rate 10%, and 1 month grace

the results was 105.505??

if i use the same formula as pmt=(10%/12,10,1000,8.3333)

having the grace profit as the FV (1000*10%/12)= 8.3333

the results are 105.443?

so i'm wondering how the installment was calculated? although i managed to have the exact same figures incase of the absence of the grace period.

i can provide more examples if anyone have an idea of the formula the system is using.

can someone help me??????

There are many ways to calculate interest and installment payments. Local laws, regulations, and business practices usually reduce the list somewhat.

I can guess what formulas may have produced the numbers you posted, but you should ask the software developer (or your computer system manager) to provide them to you. Most loan calculation software is flexible--allowing you to select from a menu of calculation options. Also ask about these settings and determine how your system is currently configured.

After you have researched your system, you should be able to match its results. Excel can be helpful, but don't rely too much on standard Excel features. For example, the PMT() function performs "monthly simple interest" payment calculations. It lacks the sophistication to handle such features as "daily simple interest" and your "grace period."

Once you are able to understand how the numbers are produced, then you can determine compliance with local laws and customs. After determining that your numbers are legal, your next priority is to determine that they match the details of the credit agreement with your borrower.

the problem is that the software developer is not responding to my emails in the most suitable way; after sending them the questions i was shocked that they requested a meeting which two of the software personal must come to me here for a face to face meeting.

i imagined that this is a good way to misuse their postion to get paid by the bank so they will not respond to any emails, and my AGM declined my meeting request due to having huge expense as he said that it won't be necessary.

nevertheless, other parties involved in the same issue are not showing high interest in knowing the formula and thats way i'm looking for answers here.

i can provide you more examples and i would mostly appreciate it if you would help me figure out the formula that gives those results for me; it will be a straight up formula isn't it??

The formula for an annuity of periodic payments of equal amount is:
A = P * r * c / (c - 1)
where:
P = Principal
R = Annual interest rate (%)
r = Rate per payment period (decimal form) = R / number of payments per year
n = Total number of payments in loan
c = (1 + r) ^ n

This gets you the payment amount when all payment periods, including the first, are equal in length.

For good business reasons, the first payment period is often set for a longer or shorter period than the standard payment period. American lenders commonly use the term "odd days" to describe this practice. Longer payment periods are said to have "long odd days", while periods that fall short of the standard are called "short odd days." When a loan has odd days, an interest adjustment is in order. This adjustment can be handled at the loan's inception, or spread across all the payments.

Based on your posts, it appears your system is trying to spread the additional interest created by long odd days. If I were designing such a system, I would perform the following steps before solving the formula above:
1. Compute a daily interest rate = annual interest rate (%) / 36500
2. Calculate the number of long odd days. Lenders have various ways to do this, but my preference is to first calculate the date that is one regular period earlier than the date of the first scheduled payment. The number of long odd days will then equal the elapsed time from the note date until the date just calculated.
3. Calculate odd-day interest = number of long odd days * daily interest rate * principal
4. Adjust the "Principal" amount (for calculation purposes, only) by adding the odd-day interest to the actual "Principal" amount.
5. Solve the formula above.

incase of a long odd days - is it as i refered to as the grace period?

like if it was more than two months??

regarding the formula i calculated one which is :

installment = ((principle+(principle*(grace period+1)/12*rate))/(1+((rate/12)))*((rate/12)))/(1-(1+((rate/12)))^-repayment period)

i think that it is working fine