Business Mathematics

Business Mathematics

Introduction
Mathematics is the soul of any business. Because a business primarily revolves around the transaction of money or products/ services that have some monetary value, involvement of money makes it extremely important to have sufficient knowledge about the basics of calculations. This is where business mathematics comes into play; It deals with the fundamentals that one needs to carry out business-related
calculations. So, here, you will learn about the mathematical tools needed for business calculations, along with their applications in solving problems.

Activity 6.0 (Work in groups)
Discuss the meanings of the following words.
(a) buying
(b) selling
(c) profit
(d) commission
discount
interest
(g) loss

6.1 Using a Multiplier when calculating Percentage Change
Under this subtopic, you will learn about multipliers and how to use them when calculating percentage changes.
The multiplier
This is the factor that increases or decreases the value of a base figure. For example, the multiplier 3 triples the base figure, yet the multiplier 0.5 halves the base figure. Many different multipliers exist in business calculations.
Activity 6.1 (a) (Work in groups)

Using the multiplier to calculate percentage changes
In Senior One, you learnt how to calculate percentage changes of given quantities. Building on this knowledge, you will now learn how to use multipliers to calculate Dercentaae chanqes.

Activity 6.1 (b) (Work in groups)
In a valuation process of three small- and medium-sized enterprises (SMEs) A, B and C, the following results were recorded for two

(a) From the table above, compute the multipliers for each SME.
(b) Using the multipliers, calculate the percentage change in value for each SME.

. Example 6.1
Adella goes on a trip with UGX 60,000 and spends 65% of it. Using multipliers,
calculate how much money she has at the end. Solution:
Spending 65% leaves her with (100% — 65%) = 35%.
35
35% as a multiplier = 0.35
So, she has 0.35 x 60,000 = UGX 21,000 at the end.

6.2 Calculating Compound Interest
Interest is the monetary charge for the privilege of borrowing money. Interest can
be simple (as discussed in Senior One) or compound.
Calculating compound interest
Activity 6.2(a) (Work in groups)
Ashaba saved UGX 100,000 in a local SACCO at an interest rate of 10% of the new amount per year, for three years.
(a) Determine the multiplier of the local SACCO.
(b) Determine the product of Ashaba’s savings and the multiplier. Comment on your result.
(c) Determine the product of your result in (b) and the multiplier. What do you notice?

(d) Determine the product of your result in (c) and the multiplier. What do you notice?
(e) What conclusion do you make from your results in (b), (c) and (d) above?
(f) By how much altogether did Ashaba’s money increase?
Activity 6.2 (b) (Work in groups)
Namuli plans to open up a savings account with a local bank. She has visited four different banks; A, B, C and D. Each bank has its own offers as indicated below.
Bank A: 1.5% compound interest per month
Bank B: 6% compound interest paid after every four months
Bank C: 9% compound interest paid after every six months
Bank D: 18% compound interest per annum
(a) Discuss and choose for her, the bank with the best offer.
(b) If she deposits UGX 100,000, how much money will she have after 2 years?
(c) In your opinion, why is saving important?
(d) Present your work to the rest of the class.

Exercise 6.2
1) Okeng deposited 2 million shillings in a bank account at a compound interest rate of 12% per annum, for 5 years. Find the interest earned by Okeng. 2) Mrs. Eilu banked money at a compound interest rate of 5% per annum. If she banked UGX 450,000, how much would she have at the end of 3 years?
3) A principal of UGX 200,000 is deposited in a savings account at 3% interest per annum, compounded annually. How much is in the account after one year, two years, and three years?
4) If UGX 3,000,000 is deposited in an account at a rate of 5% and compounded quarterly for 5 years, how much will be in the account at the end of the 5 years? 5) Mr. Mayombwe deposited UGX 1,200,000 in a account whose bank offers an interest rate of 4% per year, for 2 years. He withdrew all the money after the 2 years and deposited it in another bank account at the rate of 5% per year, and it was compounded for 4 years. What was his balance in the second account after the 4 years?

6) Assume that you are given UGX 35,000,000 shillings to open up a joint account in a certain bank. This bank offers an annual interest rate of 5% on the money in the account at the end of every year.
(a) How much money will you have to share after 5 years? (b) Find the interest earned after 5 years.
7) Owori earned UGX 5,000,000 shillings and he wanted to invest the money in a savings account. There are 3 banks; A, B, and C, each one offering a different rate. Bank A offers 1% compound interest paid monthly, Bank B offers 3% compound interest paid every three months, and Bank C Offers 12% compound interest paid annually. Which bank would he invest in? Why?

6.3 Understanding and Calculating Depreciation and Appreciation
Understanding and calculating depreciation
Activity 6.3 (a) (Work in groups)
Study your environment and list assets whose value decreases over time. Explain why their value decreases.
Activity 6.3(b) (Work in groups)

Exercise 6.3
1) A television set costs UGX 500,000. It depreciates at the rates of 5% and 3% in the first and second years, respectively. Calculate by how much it will have depreciated at the end of the second year.
2) A car costing UGX 50,000,000 depreciated at a rate of r% per annum. After 4 years, it was valued at UGX 32,805,000. Find the value of r. 3) A second-hand speedboat costs 30 million Uganda shillings. Its value depreciates at rates of 5%, 10%, and 15% in the first, second, and third years, respectively. Find its value at the end of the third year.

Understanding and calculating apprecgatlon
Activity 6.3(c) (Work in groups)
Study your environment and list assets whose value increases over time. Explain why their value increases.
Example 6.4
An article which costs UGX 15,000 appreciates at a rate of 5% per annum. Calculate its value after 2 years.
o

erefore, the value of the article after 2 years is UGX 16,537.5.
Alternatively, you can use the multiplier:
Multiplier = 1 +

• 1 + 0.05 = 1.05
  100
  The new value after 2 years is (1.05)2 x 15,000 = UGX 16,537.5.

o
Exercise 6.4
1) A piece of gold costs UGX 15 million. Its price appreciates at rates of 3%, 10% and 15% in the first, second and third years, respectively. By how much will it have gained value at the end of 3 years?
2) The tuition fees to study at a university appreciated at a rate of 10% per annum. If in the year 2021, tuition fees were UGX 1,200,000, calculate the tuition fees in the next 2 years.
6.4 Understanding and Converting Local or Foreign Currencies
In the ancient times, people exchanged goods or services for goods or services, but this had short comings. For instance, it was difficult to determine the value Of goods and services_even where the value was determined, it would be hard to divide one good, just in case it could not be exchanged for the other good fairly. Such Baroque Senior Three Mathematics

limitations e to the introduction of currency (money), which acts as a medium of exchange and a store of value. Depending on the country one lives in, one will notice that transactions are done using a variety of currencies. But different currencies have different values in terms of other currencies. nderstanding local and foreign currencies
All around the world, different countries use different currencies. Many countries have their own currency.
Activity 6.4(a) (Work in groups)
suggested materials: Uganda banknotes of different denominations Instructions
(a) State the currency name for Uganda and its symbol.
(b) Identify the different denominations of Uganda’s currency.
(c) Using any banknote in your group, study and list the features of the currency.
(d) Present your findings to the rest of the class.
Converting currency
Activity 6.4(b) (Work in groups)
Suppose that you are travelling to Kenya. You first go to a forex bureau and see the
exchange rates displa ed as below.

Example 6.5
(a) If a forex bureau buys Kenyan shilling at the rate of 36.45 Ugandan shillings
per Kenyan shilling, find the amount, in Ugandan shillings, paid out by a forex
bureau in exchange for 700 Kenyan shillings.
(b) Find the amount, in Kenyan shillings, that can be exchanged for 8,550 Ugandan shillings if the bureau sells 1 Kenyan shilling for 37.5 Ugandan shillings.

Exercise 6.5
1) Hensel wants to go abroad on a holiday
(a) If he needs dollars and the selling rate is UGX 3,706 per 1 USA. dollar, how many dollars will he get for UGX 3,706,000?
(b) If he returned with $75, find how much it is worth, in Uganda shillings, if the buying rate is UGX 3,665 for a dollar
2) A DVD player costs 190 British pound sterlings. Determine the cost of the player in UGX given the following rates; f1 = $1.03
1$ = UGX 3,665
3) The table below gives exchange rates of a certain forex bureau.

If Mr Wambi wants to visit USA, Kenya and Tanzania and wishes to get the foreign currencies for these countries in ratios of 50:30:20 for USA, Kenya and Tanzania, respectively, calculate what he can get from combining his 300 euros and 300 British pound sterlings in his foreign accounts.
4) Tusiime travelled from USA to South Africa. While in South Africa, she exchanged US$2,000 for South African rands. She then travelled to Uganda with the exchanged South African rands. How much does she have in Ugandan currency? (1 USD = 14.29 South African rands, 1 South African rand = UGX 256.70)
5) A tourist had 19,000 US dollars. How many Ugandan shillings did he get given that; 1 UK pound sterling = 1.30 US dollars and 1 pound sterling = UGX 4,770?

6.5 Understanding and calculating Hire Purchase Understanding hire purchase
Activity 6.5 (a) (Work in groups)
(a) Use a library source, the internet, or other sources to find out;
(i) the meaning of hire purchase
(ii) whether hire purchase is in operation in Uganda
(b) Make a poster about hire purchase. Share it with the rest of the class.
Calculating hire purchase
Activity 6.5(b) (Work in groups)
Obenchan wanted to buy a motorcycle which was costing UGX 4 million on cash basis. His monthly income was UGX 380,000 and he had so far saved UGX 1 million. On ISt January, 2016, he decided to negotiate with a motorcycle sales company on how to pay for the motorcycle. The sales manager accepted to sell to him the motorcycle at a cash deposit of UGX 1 million and monthly payments of UGX 100,000 for 4 years.

(a) Determine how much money he paid by the end of the 4 years.
(b) In your opinion, who of Obenchan and the sales manager, got the better deal?
Explain your answer.

Exercise 6.6
UGX 85,000
1) Kampi is to pay $100 to paint her house. An initial deposit of is to be paid and the balance is payable over a period of 6 months in equal installments, at an interest rate of 10% per month. If the exchange rate is $1 UGX 3,650, calculate the total amount of money she would have paid by the end of the 6 months.
2) A company is to procure cars worth UGX 2 billion for its employees. A quarterly hire purchase with an interest rate of 15% and payable over a period of 5 years is to be used, in equal installments.
(a) If an initial deposit of UGX 200 million is made, calculate the total amount of money that would be paid for the cars.
(b) How much would the company have saved if it had purchased by cash? 3) Given the terms:
(a) HIRE PURCHASE (payable over a period)
Deposit: UGX 2 million, and 18 monthly installments of UGX 700,000 each
(b) CASH PURCHASE: UGX 15 million with 5% discount; f ind the savings one makes by paying the cash price instead of the hire purchase price.
4) The cash price of a TV set is UGX 450,000. Under the hire purchase scheme, it can be bought by paying a deposit of UGX 250,000 and a certain number of monthly installments, each of UGX 61,250. If the hire purchase price is 10% higher than the cash price, calculate the number of installments made.
5) A dealer marks the price of a computer at UGX 4,800,000. If he charges 15% higher under the hire purchase scheme with a deposit of UGX 1,200,000 and six equal monthly installments, calculate the amount of money to be paid in each monthly installment.

6.6 Describing and Determining Mortgage of Assets
Describing mortage of assets
Activity 6.6 (Work in groups)
(a) Discuss the term “loan” as commonly used in your community.
(b) Why may some people acquire loans?
(c) List assets that can be purchased on loan in your community.
(d) What happens when a loan is not paid?

Exercise 6.7
1) A down payment of 15% of the cost of a house is to be paid and the rest paid with a compound interest rate of 5% for a period of 20 years. If the remainder is to be paid in equal monthly installments, calculate the;
(a) payment per installment
(b) extra money paid for not buying the house by cash, if the house goes for UGX 60 million
2) A house costs UGX 80 million. A deposit of 25% is required and the rest is payable in equally spread installments over a period of 15 years. Mr Enenu obtains a loan from a mortgage firm at a compound interest rate of 10%. Calculate;
(a) how much deposit he makes
(c) the total cost of the house under
(b) the amount he pays each month
the mortgage scheme
3) Mr Droti earns UGX 1.5 million per month. He intends to buy a house but his current savings are UGX 10 million. A real estate company is selling Mr Drotits dream house at UGX 50 million. A bank which offers a loan at a compound interest rate of 9% per annum, after a down payment of UGX 10 million, is willing to give Mr Droti a loan so that he pays back in installments for 5 years.
(a) How much money will Mr Droti pay for each installment?
(b) Write down the formula for computing the monthly payments. Share your answers with the rest of the class.

6.7 Calculating Income Tax when given income Tax Bands
Definition of terms used in computing income tax
There are many types of taxes which the government levies in order to get revenue and income tax is one of them. Income tax is the tax levied on an individual’s income.
Activity 6.7(a) (Work in groups)
(a) Using the internet, library, other sources find out the meanings of the following terms:
iii) Gross income
i)’ Income tax
v) Net income
ii) Taxable income iv) Non-taxable allowances vi) Income tax threshold

(c) Write down your findings and present them to the rest of the class.
(d) How can you calculate taxable income?
Calculating income tax when given income tax bands
The government fixes income tax rates from time to time. The taxable income is divided into groups called slabs and each slab has a specific rate. The amounts obtained from the various slabs are then added up to get the total payable income tax.
Activity 6.7(b) (Work in group) The following table shows the annual income taxes paid for the different annual salaries using government information as of the financial year 2020/2021.

(a) Study the table and draw a graph of income tax against annual salary.
b) State the relationship between income tax and salary.

Example 6.11 (Discuss in group)
Ashok is married with 5 children aged between 5 and 20 years. Two of the children are below 10 years, one is above 18 years, and other two are between 10 and 18 years. Given that he earns a gross monthly income of UGX 1,300,000, calculate the income tax he pays under the income tax rates below, if he claims a hospital insurance and transport refund.

2) Mrs Ssekulima earns a gross income of UGX 37,000,000 per yean The first, UGX 800,000 taxable income is taxed at 10%, the next UGX 900,000 at 20% and the balance at 30 %. She is entitled to a non-taxable monthly allowance of UGX 185,000. Calculate her;
(b) income tax
(a) taxable income

(a) taxa e Income for Olila, who earns UGX 350,000 per month as gross income.
(b) income tax as a percentage of Olila’s gross income.
4) In a certain year, the taxable amount and free pay were UGX 800,000 and UGX
250,000, respectively. A Pay As You Earn tax(P.A.Y.E) of UGX 61250 was also paid.
Calculate the;
(a) P.A.Y.E. tax as a percentage of total salary
(b) PA.Y.E. rate.
5) The schedule below shows different income categories and their corresponding tax rates.

Project Work: Visit community members in your area and have a dialogue about the
banking systems / banks available in your region. Write a report about the banking systems / banks in your region and presentit to the finance committee of your school

. ICT Activity
(a) Using a word processing software of your choice, create a table with two columns and type a shopping list of the requirements you need next term together with the estimated unit cost of each item on your list.
(b) Make a printout of your table list.
Revision Questions:
1) A piece of sculpture and painting altogether cost UGX 210,000. The painting cost is twice that of the sculpture. Find the cost of the painting. 2) The marked price of a set of curtains is UGX 75,000. If a cash discount of UGX 12.5 on every UGX 100 is offered, find the cash price of the curtains.