## Sunday, July 15, 2018

### Purpose/Objectives

Purpose of this tool is to help users to verify EMI account statement with the bank’s EMI account statement. This tool can help users to prevent bank fraudulence if any. Features like the variable rate of interest, part payment made and skip of any EMI allow the users to analyze their loan easily.

### Overview

For any loan taken, we must repay it with equated monthly installments called as EMI. This tool requires limited information like the opening balance of a loan, rate of interest, EMI amount, part payment amounts if any and the details of EMI skipped if any as input. Based on the information this tool will give the entire EMI account statement like the Opening balance of a loan, its interest, the principal amount reduced due to EMI and part payment made and closing balance for that respective month.

An educational loan of amount 3394016 is taken at an interest in 13 % pa with an EMI of 55747. EMI started from Oct-2016. Part payment of 125000 is made in Oct-2016. Then the splitting of EMI 55747 on a loan amount 3394016 at the rate of interest of 13 % per annum for Oct-2016 is 36769 (interest) and 18978 (principal amount). Here the principal amount is reduced by 143978 (125000+18978), so the new closing balance for Oct-2016 is 3250038. See the following diagram.

In Dec-2016 and Feb-2017, these two EMIs were not paid, so they are reflected in the statement. EMI of Dec-2016 was paid in May-2017 is reflected on the month May-2017. So, the total of EMI for the month May-2017 (55747) and EMI of Dec-2016 (55747) 111494 is reflected in the month of May-2017. An interest in 55747 for 5 months (Dec-16 to May-2017) at 18% interest in EMI skipped with a penalty for 427 is also reflected on this sheet for all such charges for this year.

This tool takes care of all the criteria such as:
1)      Change in EMI.
2)      Change in rate of interest.
3)      Part payment of a loan.
4)      If any EMI is skipped.
5)      The charges and interest for skipped EMI.

This interactive tool for calculating the entire EMI account statement will help all of us to verify it with the loan provider company.

## Friday, July 6, 2018

### 105-GRE Math Test - Important Key points and formulas Part - 8

#### 3) Synthetic Division:

Example-2: Divide 4x6-20x5+7x2-46x+55 by (x-5) using synthetic division method.

Solution:

1) Write all the terms in descending order:
4x6-20x5+0x4+0x3+7x2-46x+55
2) Write this polynomial in the coefficient form:
[4, -20, 0, 0, 7, -46, 55]
3) Now we will see the division using the synthetic division method.
a) Here the divisor is (x-5) so we have x-5=0, x=5.
b) Here the quotient is 4x6-20x5+0x4+0x3+7x2-46x+55 which can also be written as 4x6-205+7x2-46x+55. Here the remainder is 0.
c) So we have 4x6-205+7x2-46x+55 = (x-5) (4x5+7x-11)+0.

Example-3: Divide 5x5+20x4-2x3-8x2+3x+15 by (x+4) using synthetic division method.

Solution:
1) Write all the terms in descending order:
5x5+20x4-2x3-8x2+3x+15
2) Write this polynomial in the coefficient form:
[5, 20, -2, -8, 3, 15]
3) Now we will see the division using the synthetic division method.
a) Here the divisor is (x+4) so we have x+4=0, x=-4. b) Here the quotient is 5x5+20x4-2x3-8x2+3x+15. Here the remainder is 3.
c) So we have 5x5+20x4-2x3-8x2+3x+15 = (x+4) (5x4-2x2+3)+3.
Next part of GRE Math Test - Important Key points and formulas will be published in the next blog.