106-Detailed EMI Statement maker

Purpose/Objectives

The purpose of this tool is to help users to verify their 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 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, part payment made, and the closing balance for that respective month.

An educational loan of amount 3394016 is taken at an interest of 13 % pa with an EMI of 55747. EMI started in 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 and is reflected in the month of May 2017. So, the total EMI for the month of 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.

ANIL SATPUTE

105-GRE Math-8-Important Key points and formulas

Click here for the previous basics.

In continuation of part - 7, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued):

3) Synthetic Division: 

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

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

ANIL SATPUTE

104-GRE Math-7-Important Key points and formulas

Click here for the previous basics.

In continuation of part - 6, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued):

1) Factor Theorem: 

For a polynomial p(x), we say that (x-a) is a factor of the polynomial p(x), if we divide polynomial p(x) by (x-a), then we get the remainder as 0. i.e. p(x) = q(x) (x-a) + 0 where q(x) another polynomial called quotient (a result obtained by dividing p(x) by (x-a)).

2) Division formula in algorithm form: 

In the algorithm formula of division,  p(x) = q(x) d(x) + r(x), 

p(x) is polynomial

q(x) is quotient

d(x) is divisor

r(x) is remainder

Any polynomial can be written in the form "p(x) = q(x) d(x) + r(x)"

3) Synthetic Division: 

A few important points are to be noted to learn synthetic division.

       a) A coefficient is a real number which is the multiplicative factor of the term in the polynomial.  

Example:

1) Let the polynomial be 8x⁴-3x²+7x+3. First, write all the terms in descending order. So we write it as 8x⁴+0x³+3x²+7x+3. Now we write it in coefficient form as 8, 0, -3, 7, 3. Here, as the power of the polynomial is 4, the total number of terms of the polynomial will be 5. 

2) Let the polynomial be 7x⁵. First, write all the terms in descending order. So we write it as 7x⁵+0x⁴+0x³+0x²+0x+0. Now we write it in coefficient form as 7, 0, 0, 0, 0, 0. Here, as the power of the polynomial is 5, the total number of terms of the polynomial will be 6. 

         b) In the case of synthetic division, the divisor must be of the first degree of the form (x - a). Example (x - a) = 0, so the divisor is (x - a) with x = a.

Example: Divide 3x⁶-6x⁵+7x⁴-18x³+13x²-9x-2 by (x-2) using the synthetic division method.

Solution:
1) Write all the terms in descending order:
     3x⁶-6x⁵+7x⁴-18x³+13x²-9x-2

2) Write this polynomial in the coefficient form:
     [3, -6, 7, -18, 13, -9, -2]

3) Now we will see the division using the synthetic division method.

     a) Here the divisor is (x-2) so we have x-2=0, x=2.

   b) Here the quotient is 3x⁵+0x⁴+7x³-4x²+x+2 which can also be written as 3x⁵+7x³-4x²+x+2. here the remainder is 0.
     c) So we have 3x⁶-6x⁵+7x⁴-18x³+13x²-9x-2 = (x-2) (3x⁵+7x³-4x²+x+2)+0.

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

ANIL SATPUTE

103-Compound interest calculating tool

We will now investigate an issue related to Compound Interest.
Let's explore the concept of Compound Interest with a concrete example.
The following section addresses a common issue related to compound interest.
Now, we will focus on the computation of Compound Interest.
We will examine a typical problem that illustrates the application of Compound Interest.

Compound Interest Calculator

Formula:

A = total amount, P = the principal or the sum of money that is either deposited or borrowed, r = the annual interest rate expressed in decimal form, n = the number of compounding periods each year, and t = the time measured in years.

Example 1: If you invest Rs 7,000 in an account that offers a 5% annual interest rate compounded every two months, what will be the total amount in the account after 6 years? What will be the total interest accrued over 6 years? According to the compound interest formula, what is the annual interest amount and the effective interest rate, PCPA?

Solution:

Given:

Principal amount P = 7000, interest rate r = 0.05, n = 2 (because interest is computed every two months), and t = 6. In this case, we can utilize a logarithm to perform these calculations. Please follow the subsequent steps closely.

Take a look at the software tool designed to obtain these results systematically. Click on the image below and experiment with the outcomes for your values.

The upcoming blog will explore additional software tools for calculating compound interest.

ANIL SATPUTE

102-Tool to calculate difference between two dates (Age calculator)

Click on the following link:

A tool to get the difference between two dates

We are about to explore a handy tool that helps determine the gap between two dates, expressed in years, months, and days. To get started, let’s assess your current age — it’s precise and interactive!
👉 Click on the image below to begin:

Simply enter the necessary details in the Start Date and End Date fields, ensuring the start date precedes the end date. This tool calculates the duration between two dates in years, months, and days.

Whether you're interested in your current age, the age you were when you graduated, or the age gap between you and a relative, this calculator delivers quick and precise results. It's a straightforward yet effective tool for various practical scenarios.

 ANIL SATPUTE

101-GRE Math-6-Important Key points and formulas

Click here for the previous basics.

In continuation of part - 5, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued): 

4) (x - a) (x - b) = x (x - b) - a (x - b)
                         = x ² - b x - a x + ab
                         = x ² - (a + b) x + ab
Generally, we call x ² as the first term, (a + b) x as the middle term, and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "+" so factorize the product of the coefficient of the first term (here it is 1) and the last term in such a way that the SUM of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x ² - 10 x + 21.

a) Step-1: Here sign of the last term 21 is "+"
b) Step-2: The coefficient of the first term is 1 and the last term is 21, so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "+", their addition is -3 - 7 = -10 which is the coefficient of the middle term.  
                         = x ² - 10 x + 21
                         = x ² - (3 + 7) x + (3 x 7)
                         = x ² - 3 x - 7 x + (3 x 7)
                         = x (x - 3) - 7 (x - 3)
                         = (x - 3) (x - 7)
c) Step-3: So the factors of x ² - 10 x + 21 are (x - 3) and (x - 7) 

Example-2:

Factorize: 8 x ² - 14 x + 5.

a) Step-1: Here sign of the last term 5 is "+"
b) Step-2: The coefficient of the first term is 8 and the last term is 5, so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2, and 5 and as the sign of the last term is "+", so, we take two factors in such a way that their sum will be 14. Here 2, 2, 2, and 5 will give us 4 and 10. So, here addition is -4 - 10 = -14 which is the coefficient of the middle term.  
                         = 8 x ² - 14 x + 5
                         = 8 x ² - (4 + 10) x + 5
                         = 8 x ² - 4 x - 10 x + 5
                         = 4 x (2 x - 1) - 5 (2 x - 1)
                         = (4 x - 5) (2 x - 1)
c) Step-3: So the factors of 8 x ² - 14 x + 5 are (2 x - 1) and (4 x - 5).

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

ANIL SATPUTE

100-GRE Math-5-Important Key points and formulas

Click here for the previous basics.

In continuation of part - 4, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued): 

3) (x - a) (x + b) = x (x + b) - a (x + b)
                          = x ² + b x - a x - ab
                          = x ² - (a - b) x - ab
Generally, we call x ² as the first term, (a + b) x as the middle term, and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "-" so factorize the product of the coefficient of the first term (here it is 1) and the last term in such a way that the DIFFERENCE of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x ² - 4 x - 21.

a) Step-1: Here sign of the last term 21 is "-"
b) Step-2: The coefficient of the first term is 1 and the last term is 21, so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "-", their subtraction is 3 - 7 = -4 which is the coefficient of the middle term. (Note: Here, the coefficient of the middle term is positive so we took it as 3 - 7).  
                         = x ² - 4 x - 21
                         = x ² + (3 - 7) x - (3 x 7)
                         = x ² + 3 x - 7 x - (3 x 7)
                         = x (x + 3) - 7 (x + 3)
                         = (x - 7) (x + 3)
c) Step-3: So the factors of x ² - 4 x - 21 are (x + 3) and (x - 7) 

Example-2:

Factorize: 8 x ² - 18 x - 5.

a) Step-1: Here sign of the last term 5 is "-"
b) Step-2: The coefficient of the first term is 8 and the last term is 5, so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2, and 5 and as the sign of the last term is "-", so, we take the two factors in such a way that their difference will be 18. Here 2, 2, 2, and 5 will give us 2 and 20. So, here subtraction is 2 - 20 = -18 which is the coefficient of the middle term.  
                         = 8 x ² - 18 x - 5
                         = 8 x ² + (2 - 20) x - 5
                         = 8 x ² + 2 x - 20 x - 5
                         = 2 x (4 x + 1) - 5 (4 x + 1)
                         = (2 x - 5) (4 x + 1) 
c) Step-3: So the factors of 8 x ² - 18 x + 5 are (2 x - 5) and (4 x + 1).

In the next part, we will see the remaining 1 type in detail. These 1 types are given below.
4) (x - a) (x - b) = x ² - (a + b) x + ab

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

ANIL SATPUTE