MASENO SCHOOL

Topic 6: Commercial Arithmetic II

By Mr. Patrick Mboya
1. A business person invested Ksh. 350,000 in a bank that pays simple interest at the rate of 10% per annum
for 1 12 years. Upon maturity, the business person reinvested the amount collected in another bank that pays
compound interest at the rate of 10% per annum for 2 years. Calculate the total interest on the amount
invested.

2. A man invested Ksh 240,000 in bank A at a simple interest rate of 12% p.a for 3 years and Ksh 200,000
in bank B at a simple interest rate of 14% p.a for the same duration. Which bank gave a greater return?

3. A businesswoman borrowed Ksh. 240,000 from a financial institution that charges compound interest of
12% p.a for five years. She used the money to purchase a piece of land that appreciates at the rate of 15%
p.a. If she sold the piece of land after five years, determine the amount of profit she made.

4. A car was purchased in January 2010 for Ksh. 850,000 and sold in December 2014 for Ksh. 425,000.
Calculate its rate of depreciation.

5. A refrigerator can be bought in cash for Ksh. 35,000. The same refrigerator can be purchased on hire
purchase terms by first paying a deposit of Ksh 6,000 followed by 24 equal monthly instalments of
Ksh. 1,500. Calculate the hire purchase price and the carrying charge

6. The cash price of a radio is Ksh. 52,000. Its hire purchase price is 20% more and can be settled by paying
Ksh. 2,430 for 18 months plus a deposit. Calculate the amount of deposit required.

7. A mobile phone can be purchased in cash Ksh. 30,000 or by paying Ksh. 1,750 for 24 months. Calculate
the rate of interest charged on instalment buying. Give your answer correct to 2 decimal places.

8. Determine the amount of interest when Ksh. 320,000 is invested in a bank that pays compound interest
quarterly at the rate of 12% p.a for 3 years.

9. Rono invested a sum of money Sh. P at 24% per annum simple interest for 8 years and realised that he got
the same amount as Wekesa who invested Sh. 2P for 4 years at compound interest. Calculate the rate of
interest per annum Wekesa enjoyed.

10. Momanyi deposited Sh. 250,000 in a fixed account for a period of 24 months. The bank pays compound
interest on quarterly basis. At the end of this period, Momanyi’s account had Sh. 316,693. Determine the
rate at which interest is paid per annum.

11. The cash price of a fridge is Sh. 30,000. Anne bought the fridge on hire purchase by paying a deposit of
Sh. 7,500 and 14 monthly instalments of Sh. 1,875 each. Calculate the monthly rate of interest she was
charged. Give your answer to 2 decimal places.

12. The cash price of a television set is Ksh. 36,000. Compound interest of 3.4366% per month is charged on
the balance when the television set is bought on hire purchase terms by paying a deposit of Ksh. 8,000 and
the instalments cleared in 12 months. Calculate the amount of each instalment to the nearest shilling.

13. Eliud Kipchoge is an athlete who feels that his playing career will last 5 years. To prepare for his future,
he deposits Ksh 480 000 at the end of each year for 5 years in an account paying 6% compounded annually.
How much will he have on deposit after 5 years?

14. Juma deposited Sh. 45 000 in a bank which paid interest at 12% p.a compounded monthly. Calculate the
amount of interest after 3 years.
 Commercial Arithmetic II By Mr. Patrick Mboya

15. The cash price of a fridge is Ksh. 41,400. Joe buys the fridge on hire purchase terms by paying a deposit
of Ksh.15,960. Simple interest of 15% p.a is charged on the balance. If Joe pays the balance in 24 equal
installments, calculate the amount of each instalment.

16. The price of a new car is Ksh.900,000. If its value depreciates at a constant rate to Ksh.450,000 in 4 years,
find the annual rate of depreciation. Give your answer to one decimal place.

17. The table below shows monthly income tax rates for a certain year.

Monthly income (in KSh) Tax rate in each shilling

0  11 180 10%
11 181  21 680 15%
21 681  32 230 20%
32 231  42 830 25%
Above 42 830 30%

In that year, a monthly personal relief of KSh. 1 280 and an insurance relief at 3% of the premium was
allowed. A civil servant earns a gross salary of KSh. 40 000 and pays Ksh. 4 200 towards his medical
insurance cover. Calculate the amount of tax that he pays.
18. The table below shows income tax rates in the year 2018.

Monthly Income ( Ksh) Percentage Tax Rates

Up to 9680 10
9681  18800 15
18801  27920 20
27921  37040 25
37041  46160 30
46161 and over 35
a) Calculate the total tax payable in the first four bands.
b) A civil servant’s taxable income lies in the fifth band. She is entitled to a monthly personal tax
relief of Ksh. 1058. In a certain month of the year, her net tax was Ksh. 6924 . Calculate the
amount of her taxable income.

19. The table below shows monthly income tax rates for a certain year.

Monthly Income (Ksh) Percentage Tax Rates

Under 9681 10%
From 9681 but under 18801 15%
From 18801 but under 28021 20%
From 28021 but under 37141 25%
37041 and above 30%

A civil servant pays PAYE amounting to KSh. 4899. He is entitled to a monthly personal relief of
Ksh. 1056 and an insurance relief at 10% of his monthly premiums. Every month, he pays Ksh. 4200
towards her education insurance policy. Calculate the amount of her taxable income.

20. The cash price of a T.V set is Ksh. 26000. Linda bought the set on hire purchase terms by paying a
deposit of Ksh. 6000 and the balance by 24 equal monthly instalments of Ksh. 1045.30. Find the
compound rate of interest per year.
2
 Commercial Arithmetic II By Mr. Patrick Mboya

Answers
1. 137025 8. 136243.4838 15. 2756
2. A = 36% B = 42% 9. 9.923% pa 16. 15.9%
3. 59763.721 10. 12.00% 17. 5339.50
4. 12.94% 11. 1.11% pm 18. Ksh 6440, Ksh 42180
5. HP = 42000, CC = 7000 12. 2834 19. 36800
6. 18660 13. 2705804.621 20. 12.00% pa
7. 1.55% pm 14. 19384.59526