ZeePedia

Applications of Basic Mathematics Part 5:DECREASE IN RATE

<< Applications of Basic Mathematics Part 4:PERCENTAGE CHANGE
Applications of Basic Mathematics:NOTATIONS, ACCUMULATED VALUE >>
img
MTH001 ­ Elementary Mathematics
LECTURE 17
Applications of Basic Mathematics
Part 5
OBJECTIVES
The objectives of the lecture are to learn about:
·
·
Discount
·
Simple and compound interest
·
Average due date, interest on drawings and calendar
REVISION LECTURE 5
A chartered bank is lowering the interest rate on its loans
from 9% to 7%.
What will be the percent decrease in the interest rate on a given
balance?
A chartered bank is increasing the interest rate on its loans from
7% to 9%
What will be the percent increase in the interest rate on a given
balance?
As we learnt in lecture 5, the calculation will be as follows:
Decrease in interest rate = 7-9 = -2 %
% decrease = -2/9 x 100 = -22.2 %
Increase in interest rate = 9-7 = 2 %
% decrease = 2/7 x 100 = 28.6 %
The calculations in Excel are shown in the following slides:
DECREASE IN RATE
Data entry
Cell F4 = 9
Cell F5 = 7
Formulas
Formula for decrease in Cell F6: = =F5-F4
Formula for % decrease in Cell F7: =F6/F4*100
Results
Cell F6 = -2%
Cell F7 = -22.2%
INCREASE IN RATE
Data entry
Cell F14 = 7
Cell F15 = 9
Formulas
Formula for increase in Cell F16: =F15-F14
Formula for % increase in Cell F17: =F16/F14*100
Results
Cell F16 = 2%
Cell F17= 28.6%
Page
111
img
MTH001 ­ Elementary Mathematics
The Definition of a Stock
Plain and simple, stock is a share in the ownership of a company. Stock
represents a claim on the company's assets and earnings. As you acquire more
Page
112
img
MTH001 ­ Elementary Mathematics
stock, your ownership stake in the company becomes greater. Whether you say
shares, equity, or stock, it all means the same thing.
Stock yield
With stocks, yield can refer to the rate of income generated from a stock in the form
of regular dividends. This is often represented in percentage form, calculated as the
annual dividend payments divided by the stock's current share price.
Earnings per share (EPS)
The EPS is the total profits of a company divided by the number of shares. A company with
$1 billion in earnings and 200 million shares would have earnings of $5 per share.
Price-earnings ratio
A valuation ratio of a company's current share price compared to its per-share earnings.
Calculated as:
For example, if a company is currently trading at $43 a share and earnings over the
last 12 months were $1.95 per share, the P/E ratio for the stock would be 22.05
($43/$1.95).
Outstanding shares
Stock currently held by investors, including restricted shares owned by the
company's officers and insiders, as well as those held by the public. Shares that have
been repurchased by the company are not considered outstanding stock.
Net current asset value per share(NCAVPS)
NCAVPS is calculated by taking a company's current assets and subtracting the total
liabilities, and then dividing the result by the total number of shares outstanding.
Current Assets
The value of all assets that are reasonably expected to be converted into cash within one
year in the normal course of business. Current assets include cash, accounts receivable,
inventory, marketable securities, prepaid expenses and other liquid assets that can be
readily converted to cash.
Liabilities
A company's legal debts or obligations that arise during the course of business operations.
Market value
The price at which investors buy or sell a share of stock at a given time
Face value
Page
113
img
MTH001 ­ Elementary Mathematics
Original cost of a share of stock which is shown on the certificate. Also referred to as "par
value."
Face value is usually a very small amount that bears no relationship to its market price.
Dividend
Usually, a company distributes a part of the profit it earns as dividend.
For example: A company may have earned a profit of Rs 1 crore in 2003-04. It
keeps half that amount within the company. This will be utilised on buying new
machinery or more raw materials or even to reduce its borrowing from the bank.
It distributes the other half as dividend.
Assume that the capital of this company is divided into 10,000 shares. That
would mean half the profit -- ie Rs 50 lakh (Rs 5 million) -- would be divided by
10,000 shares; each share would earn Rs 500. The dividend would then be Rs
500 per share. If you own 100 shares of the company, you will get a cheque of
Rs 50,000 (100 shares x Rs 500) from the company.
Sometimes, the dividend is given as a percentage -- i e the company says it has
declared a dividend of 50 percent. It's important to remember that this dividend is
a percentage of the share's face value. This means, if the face value of your
share is Rs 10, a 50 percent dividend will mean a dividend of Rs 5 per share
BUYING SHARES
If you buy 100 shares at Rs. 62.50 per share with a 2% commission, calculate
your total cost.
Calculation
100 * Rs. 62.50 = Rs. 6,250
0.02 * Rs. 6,250 =
125
Total
= Rs. 6,375
RETURN ON INVESTMENT
Suppose you bought 100 shares at Rs. 52.25 and sold them after 1 year at Rs.
68. With a 1% commission rate of buying and selling the stock and 10 %
dividend per share is due on these shares. Face value of each share is 10Rs.
What is your return on investment?
Bought
Page
114
img
MTH001 ­ Elementary Mathematics
100 shares at Rs. 52.25 = 5,225.00
Commission at 1%
=
52.25
Total Costs
=5,225 + 52.25 = 5,277.25
Sold
100 shares at Rs. 68
= 6,800.00
Commission at 1%
= - 68.00
Total Costs Sale
= 6,800 ­ 68 = 6,732.00
Gain
Net receipts
= 6,732.00
Total cost
= - 5,277.25
Net Gain
= 6,732 ­ 5,277.25 =1,454.75
Dividends (100*10/10)
=  100.00
Total Gain
= 1,454.75 + 100 = 1,554.75
Return on investment
= 1,554.75/5,277.25*100
= 29.46 %
The calculations using Excel were made as follows:
BOUGHT
Data entry
Cell B21: 100
Cell B22: 52.25
Formulas
Formula for Cost of 100 shares at Rs. 52.25 in Cell B23: =B21*B22
Formula for Commission at 1% in Cell B24: =B23*0.01
Formula for Total Costs in Cell B25: =B23+B24
Results
Cell B23 = 5225
Cell B24 = 52.25
Cell B25 = 5277.25
Page
115
img
MTH001 ­ Elementary Mathematics
SOLD
Data entry
Cell B28: 68
Formulas
Formula for sale of 100 shares at Rs. 68 in Cell B29: =B21*B28
Formula for Commission at 1% in Cell B30: =B29*0.01
Formula for Total Sale in Cell B31: =B29-B30
Results
Cell B29 = 6800
Cell B30 = 68
Cell B31 = 6732
Page
116
img
MTH001 ­ Elementary Mathematics
GAIN
Formulas
Formula for Net receipts in Cell B34: =B31
Formula for Total cost in Cell B35: =B25
Formula for Net Gain in Cell B36: =B31-B25
Formula for % Gain in Cell B37: =B36/B35*100
Results
Cell B34 = 6732
Cell B35 = 5277.25
Cell B36 = 1454.75
Cell B37 = 27.57
DISCOUNT
Discount is Rebate or reduction in price.
Discount is expressed as % of list price.
Example
List price = 2200
Discount Rate = 15%
Discount?
= 2200 x 0.15= 330
Calculation using Excel along with formula is given in the following slide:
NET COST PRICE
Net Cost Price = List price - Discount
Example
List price = 4,500 Rs.
Discount = 20 %
Netcost price?
Page
117
img
MTH001 ­ Elementary Mathematics
Net cost price = 4,500 ­ 20 % of 4,500
= 4,500 ­ 0.2 x4,500
=4,500 ­ 900
= 3,600 Rs.
Calculation using Excel along with formula is given in the following slide:
SIMPLE INTEREST
P = Principal
R = Rate of interest per annum
T = Time in years
I = Simple interest
then
I = P. R. T / 100
Thus total amount A to be paid at the end of T years = P + I
Example
P = Rs. 500
T = 4 years
R =11%
Find simple interest
I = P x T x R /100
= 500 x 4 x 11/100
= Rs. 220
Calculation using Excel along with formula is given in the following slide:
Page
118
img
MTH001 ­ Elementary Mathematics
COMPOUND INTEREST
Compound Interest also attracts interest.
Example
P = 800
Interest year 1= 0.1 x 800= 80
New P = 800 + 80 = 880
Interest on 880 = 0.1 X 880 = 88
New P = 880 + 88 = 968
Calculation using Excel along with formula is given in the following slide:
Page
119
img
MTH001 ­ Elementary Mathematics
Co
mpound Interest Formula
S = Money accrued after n years also called compound amount
P = Principal
r = Rate of interest
n = Number of periods
S = P(1 + r/100)^ n
Compound interest = S - P
Example
Calculate compound interest earned on Rs. 750 invested at 12% per annum for
8 years.
S= P(1+r/100)^8
= 750(1+12/100)^8
=1857 Rs
Compound interest = 1857 ­ 750 = 1107 Rs
Page
120
img
MTH001 ­ Elementary Mathematics
Calculation using Excel along with formula is given in the following
slide
Page
121
Table of Contents:
  1. Recommended Books:Set of Integers, SYMBOLIC REPRESENTATION
  2. Truth Tables for:DE MORGAN’S LAWS, TAUTOLOGY
  3. APPLYING LAWS OF LOGIC:TRANSLATING ENGLISH SENTENCES TO SYMBOLS
  4. BICONDITIONAL:LOGICAL EQUIVALENCE INVOLVING BICONDITIONAL
  5. BICONDITIONAL:ARGUMENT, VALID AND INVALID ARGUMENT
  6. BICONDITIONAL:TABULAR FORM, SUBSET, EQUAL SETS
  7. BICONDITIONAL:UNION, VENN DIAGRAM FOR UNION
  8. ORDERED PAIR:BINARY RELATION, BINARY RELATION
  9. REFLEXIVE RELATION:SYMMETRIC RELATION, TRANSITIVE RELATION
  10. REFLEXIVE RELATION:IRREFLEXIVE RELATION, ANTISYMMETRIC RELATION
  11. RELATIONS AND FUNCTIONS:FUNCTIONS AND NONFUNCTIONS
  12. INJECTIVE FUNCTION or ONE-TO-ONE FUNCTION:FUNCTION NOT ONTO
  13. SEQUENCE:ARITHMETIC SEQUENCE, GEOMETRIC SEQUENCE:
  14. SERIES:SUMMATION NOTATION, COMPUTING SUMMATIONS:
  15. Applications of Basic Mathematics Part 1:BASIC ARITHMETIC OPERATIONS
  16. Applications of Basic Mathematics Part 4:PERCENTAGE CHANGE
  17. Applications of Basic Mathematics Part 5:DECREASE IN RATE
  18. Applications of Basic Mathematics:NOTATIONS, ACCUMULATED VALUE
  19. Matrix and its dimension Types of matrix:TYPICAL APPLICATIONS
  20. MATRICES:Matrix Representation, ADDITION AND SUBTRACTION OF MATRICES
  21. RATIO AND PROPORTION MERCHANDISING:Punch recipe, PROPORTION
  22. WHAT IS STATISTICS?:CHARACTERISTICS OF THE SCIENCE OF STATISTICS
  23. WHAT IS STATISTICS?:COMPONENT BAR CHAR, MULTIPLE BAR CHART
  24. WHAT IS STATISTICS?:DESIRABLE PROPERTIES OF THE MODE, THE ARITHMETIC MEAN
  25. Median in Case of a Frequency Distribution of a Continuous Variable
  26. GEOMETRIC MEAN:HARMONIC MEAN, MID-QUARTILE RANGE
  27. GEOMETRIC MEAN:Number of Pupils, QUARTILE DEVIATION:
  28. GEOMETRIC MEAN:MEAN DEVIATION FOR GROUPED DATA
  29. COUNTING RULES:RULE OF PERMUTATION, RULE OF COMBINATION
  30. Definitions of Probability:MUTUALLY EXCLUSIVE EVENTS, Venn Diagram
  31. THE RELATIVE FREQUENCY DEFINITION OF PROBABILITY:ADDITION LAW
  32. THE RELATIVE FREQUENCY DEFINITION OF PROBABILITY:INDEPENDENT EVENTS