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Commercial Arithmetic 2 Questions
1. The table below shows the rate at which income tax is charged for all taxable income.
INCOME RATE IN EXCH TWENTY SHILLINGS
On the first shs.116 160 10%
On the next shs.109 440 15%
On the next shs.109 440 20%
On the next shs.109 440 25%
On all income over shs.444 480 30%
Mr. Nyongesa earns a basic salary of sh.54, 450 per month. He is housed by the company and therefore 15% of his monthly salary is added to the basic salary as a taxable income. He is also given taxable medical and transport allowances of shs.4,000 and shs.2,000 per month respectively. He is entitled to a family relief of sh.1, 100 per month.
(a) Calculate Nyongesa’s annual taxable income (3 mks)
(b) Calculate his monthly P.A.Y.E after the relief (5 mks)
(c) If 20% of his basic salary goes towards deductions, determine his monthly income. (2 mks)
2. All employees of silver springs enterprises pay income tax at the rate shown in the table below.
Taxable income (p.a) | Rate sh. Per K₤ |
1 – 3780 3781-7560 7561-11,340 11,341-OVER | 2 3 4 5 |
Mr. Mooka earns a basic salary of sh.12,150 and a house allowance of sh.2800 per month. He is
entitled to a family relief of sh.450 per month. A part from income tax the following deductions are also made from his monthly pay.
- Servicing loan payment sh.450
- Hospital fund sh.260
- Sacco contribution sh.120
Determine Mr. Mooka’s net monthly income. (10 marks)
3. The taxation rates for income earned in a certain year were as follows:
Income Tax Rate
K£ p.a Kshs. Per £
1 – 4512 2
4513 – 9024 3
9025 – 13536 4
13537 – 18048 5
18049 – 22560 6
Over 22560 6.5
After a personal relief of Kshs.1056 per month, Otieno paid tax amounting to Kshs.18,152 that year.
a) How much tax would he have paid if he did not have the personal relief (2 mks)
b) Find his taxable income in K£ that year (5 mks)
c) If Otieno receives allowances amounting to 18% of the taxable income. Calculate his monthly basic salary in Kshs. (3 mks)
4. Chepkemoi bought a new washing machine for Kshs.420,000. Its value depreciated over
the next 5years at the following rates; 15%, 13%, 12%, 9% and 7%. For the next 6 years,
the rate of depreciation remained constant at 5% then the rate of depreciation remained at 4%
each. How long did it take for the value of the washing machine to be ^{1}/_{3} of its original value?
5. The table below shows income tax rates for the year 2006
Taxable income in shs. Pa | Rate of tax in % |
1 – 120,000 | 10 |
120,001 – 240,000 | 15 |
240,001 – 360,000 | 25 |
360,001 – 480,000 | 35 |
Over 480,000 | 50 |
Nafula is married and claims a tax relief of shs.1,120 per month. She stays in a company house
For which she pays a nominal rent of shs.1200 per month. She found that in a particular month,
her employer deducted shs.4830 as tax. If she is entitled to a maximum insurance policy; relief
of shs.600 per month. Calculate her monthly salary. (10mks)
6. The figure below represents two pulley wheels, centres A and B with a rubber band
CDEFGHC stretched round them. Radius of wheel centre A = 16cm, AB = 30cm. CD,
GF are tangents to the circles < CAB = 86.3°
a) calculate the length of the belt CD
b) Find the angle ABD
c) Find the length of the belt that would go round the pulleys (CDFGHC)
7. In the figure below, ABCD is a cyclic quadrilateral and BD is a diagonal. EADF is a straight line,
CDF = 68^{o}, BDC = 45^{o} and BAE = 98^{o}.
Calculate the size of:
a) ABD.
b) CBD
8. A customer deposited Ksh.15,500 in a savings account. Find the accumulated amount
after 3½ years if interest was paid at 16% per annum compounded semi-annually
9. A retailer mixes three types of rice, Bismatti costing shs.120 per tin with Pishori costing shs.150
per tin and Ahero rice costing shs.80 per tin in the ratio x : 1 : 2 respectively. If he sells the
mixture at shs.137.50 per tin making a profit of 25%. Calculate the value of x.
10. Ashanti is a saleswoman and earns a commission on sales based on the monthly rates shown
in the table below:-
Sales (Kshs) | Commission rate % of sales |
The first 5000 | 10% |
The next 3000 | 15% |
Sales above 8000 | 20% |
In addition, she earns a basic monthly pay of Kshs.6700. During a certain month, she earned
a total salary amounting to Kshs.8368. How much worth of sales did she make?
11. The table below shows the annual income tax rates for a certain year.
Total income per month in Kshs. | Rates in Kshs. Per £ |
1-10164 10165 – 19740 19741 – 29316 29317 – 33892 388983 and above | 2 3 4 5 6 |
Automatic personal relief shs.1162 |
Kiptoo earns a monthly salary of Kshs.25000. He is entitled to house and medical allowances
of Kshs.12000 and Kshs.3000 respectively
Calculate:
(a) His taxable income per month
(b) His monthly tax payable
(c)His annual tax payable
12. A company employee earns a basic salary of Kshs.25,000 and is also given taxable allowances
amounting to Kshs.10,480.
Monthly taxable income | Rate in Kshs. /Pound |
1- 4350 4351 – 8900 8901 – 13455 13451 – 18005 18006 and above | 2 3 4 5 6 |
Using the table of taxation above:-
(a) Calculate the employee’s taxable income
(b) If the employee is entitled to a personal tax relief of Kshs.800 per month, determine the net tax
(c) If the employee was given 40% increase in his income, calculate the percentage increase
in his income tax
13. A certain amount of money was invested at compound interest of 10% compounded
every two years for ten years. Given that the investor invested a total of 500,000/= at the
end of the ten years, find the amount of money invested to the nearest shillings
14. The cash price of a T.V set is Ksh. 26,000. Linda bought the set on hire purchase terms by
paying a deposit of Ksh. 6,000 and the balance by 24 equal monthly installments of
Khs. 1,045.30. Find the compound rate of interest per year.
.
15. What would Kshs.15000 amount to after 3years at 16% per annum compounded quarterly?
16 . Income rates for income earned were charged as follows:
Income in Kshs. p.m Rate in Kshs. per sh.20
1- 8400 2
8401- 18,000 3
18,001- 30,000 4
30,000 – 36,000 5
36,001 – 48,000 6
48,001 and above 7
A civil servant earns a monthly salary of Ksh.19,200. His house allowance is Ksh12,000 per
month. Other allowces per month are transport Ksh.1300 and medical allowance Ksh.2300.
He is entitled to a family relief of Kshs. 1240 per month.
Determine:
a) (i) His taxable income per month.
(ii) Net tax. b) In addition, the following deductions were made
NHIF shs. 230
Service charge Kshs. 100
Loan repayment Kshs. 4000
Co-operative shares of Kshs. 1200.
Calculate his net salary per month.
17. Use the taxation rates in the table below to answer the questions that follow;-
Taxable income in K £ p.a | Rate % per K£ |
1-4500 4501-7500 7501 – 10500 10501 – 13500 13501 – 16500 0ver 16500 | 10 15 20 25 30 35 |
The manager of a certain company is entitled to a monthly personal relief of shs.3000
and her tax (PAYE) is kshs.9000 per month she is also deducted NHIF shs.350 per month,
WCPS shs.800 per month and cooperative shares shs.1200 per month, calculate
(a) The managers total deductions per month
(b) Total tax per month
(c) The manager’s annual gross salary
(d) The manager’s monthly basic salary if her monthly allowance and medical allowances
are 10000 and 2000 shillings
18. The table below shows the income tax for a certain year;
Monthly taxable income (Kshs.) | Tax rates (%) |
1- 9680 9681- 18800 18801 – 27920 27921 – 37040 37940 and above | 10% 15% 20% 25% 30% |
In that year, Odero paid a net tax of Kshs.5,512 per month. His total monthly taxable allowances
amounted to Kshs.15,220 and he was entitled to a monthly personal relief of kshs.1,162.
Every month the following deductions were made;
N.H.I.F Kshs.320
Union dues Kshs.200
Co-operative shares Kshs.7,500
(a) Calculate Odero’s monthly basic salary in Kshs
(b) Calculate his monthly salary
19. (a) A car is worth shs.800,000 when new. During the first year it depreciates by 20%
of its value and in the second it deprecates by 5% of its value at the start of the year.
During the third, fourth and fifth year, depreciation rate is 10%. How much less will
it cost at the end of the fifth year?
(b) Find by how much the compound interest will exceed simple interest on shs.3,000
for two years at 15% per year
20. The table below shows the income tax rates:
Income per month (K£) Rate in Kshs per £
1 – 325 2
326 – 975 3
976 – 1300 5
1301 – 1625 6
Over 1625 7.50
Mr. Misoi is a public servant who lives in a government house and pays a nominal rent of Kshs.1,220 per month. He earns a basic salary of Kshs. 24,800 and a house allowance of Kshs.12,000 per month. He is entitled to a monthly relief of kshs.1620.
(a) Calculate his monthly;
(i) Taxable income in K£
(ii) Tax payable without relief
(iii) Tax after relief
(b) Apart from the income tax. The following monthly deductions are made from his earnings
-HELB loan repayment Kshs.2400
– Health insurance fund Kshs.1200
– 2% of Basic salary union fee
Calculate:- (i) the total monthly deduction made on Mr. Misoi’s income
(ii) Mr. Misoi’s net income per month
21. Joseph bought a camera on hire purchase (H.P) term by paying a deposit of shs.7200
and cleared the balance in 24 equal monthly installments each of 1250.
(a) find the hire purchase price of the camera
(b) the hire purchase price of the camera is 24% higher than the cash price. Find the
cash price of the camera
(c) Kangara took a loan from a financial institution and bought the camera with cash.
He repaid the loan at 18% p.a compound interest at the end of the two years. Find
the total interest paid by Kangara.
22. Income tax for all the income earned was charged at the rates shown.
Total Income p.a (K.£) | Rate in sh per K£ |
1 – 1980 1981 – 3960 3961 – 6440 6441 – 7920 7921 – 9900 Excess of 9900 | 2 3 5 7 9 10 |
(a) Wanyonyi earned a salary of Kshs.10,500 per month. In addition he was given a house
allowance of Kshs. 6500 per month. He got tax relief of Kshs. 300 per month.
Find (i) His taxable income p.a (ii) Income tax he pays per month. (b) A part from income tax the following deductions are made per month. NHIF of Kshs.320,
widow and pension scheme of 2% of his gross salary. Calculate his net monthly pay.
Commercial Arithmetic 2 Answers
1 |
a)
b)
Total annually Monthly Less relief 1100.00 Net tax payable c)
Total deductions Monthly income |
M_{1} M_{1} A_{1}
M_{1}
M_{1}
M_{1}
M_{1}
A_{1}
B_{1}
B_{1} |
1^{st} and 2^{nd} slabs
3^{rd} and 4^{th} slabs
last slab
Subtraction of relief
Total deductions |
1. After 1^{st} year = 95 x 4200000)
100
= Shs.357,000
After 2^{nd} year = ( 87 x 357000)
100
= sh310590
After 3^{rd} year = (88 x 310590
100
= shs.273319.20
After 4^{th} year = ( 91 x 273319.20)
100
=shs.248720.50
After 5^{th} year = (248720.50 x 93)
100 = shs.231310
The next 6years
A = 231310 (1- 0.05)^{6} = 170034.10
Then 140000 = 170034.10 (1-0.04)^{n}
(0.96)^{n} = 140000 = 0.8234
170034.10
n = log 0.8234
log 0.96
= 0.0844 = 4.76yrs
0.01773
Total no. of years = 5 + 6 + 4.76yrs = 15.76years
2. Gross tax = 4830 + 1120 + 600 = sh 6550 per month
Annual gross tax = 6550 X 12= 78,600
10 X 120,000 = sh.12,000
100
15 X 120,000 = sh.18,000
100
25 X 120,000 = sh. 30,000
100
Re. tax = 78600 – (12000 + 18000+30000)
=78600 – 60,000 = 18,6000
35 X x =18,600
100
0.35x = 18,600
x = sh 53142.86
Taxable income p.a = 36,000+53142.86
=sh.412142.86
Monthly salary = 413142.86 + 12,000
12
= 34428.57 + 1200 = Sh 35628.57
3. a) Sin 86.3° = ^{XB}/_{AB}
Sin 86.3°= ^{XB}/_{30}
XB = 30sin86.3°
XB = CD = 29.93746855 cm
b) < ABX = 90° - 86.3°
= 3.7°
< ABD = 3.7° + 90°
= 93.7°
c) < DBF obtuse = 360° - 187.4°
= 172.6°
Arc DEF = ^{ø}/_{360}
D or ^{ø}/_{360 }x2r
But cos 86.3° = ^{AX}/_{AB}
Cos 86.3° = ^{AX}/_{30}
AX = 1.935969248 cm
DB = 16 – 1.935969248 = 14.06403075 cm
Arc DEF = ^{172.6°/}_{360°} x ^{22}/_{7} x 14.06403075
= 106807.8751
2520
= 42.38407742 cm
Arc CGH
< reflex CAG = 360° - (2x 86.3°)
= 187.4°
Arc CGH = ^{187.4°/}_{360°} x2 x ^{22}/_{7} x 16
= 131,929.6
2520
= 52.35301587 cm
Total length of belt to go round the belt
= CD + DEF + GF + CHG
= 29.93746855 + 42.38407742 + 29.93746855 + 52.35301587
= 154.6120304 cm
4. ∠ABD = 31^{0}
∠ CBD = 37^{0}
5. A = 15,000(1 + ^{8}_{/100})^{7}
= Ksh.25,707
6. Principle = 30,000 – 6,000
= 24,000/=
Amount = 18 x 2000
= 36,000/=
A = P 1 + r
100
6,000 = 24000 1 + r
100
36000 = 1 + r
24000 100
3 = 1 + r
2 00
1 + r = 18 1.8
100
1 + r = 1.023
100
r = 0.023
100
⇒2.3%
7. Commission earned Kshs. (8368 – 6700) = Kshs. 1668/=
let sales in 3rd bracket be y
^{10}/_{100} x 5000) + (^{15}/_{100} x 3000) + (^{20}/_{100} x y) = 1668
500 + 450 + 0.2y = 1668
0.2y = 1668 – 950 = 718
y = ^{718}/_{0.2} = 35%
Total sales = (8000 + 3590)
= shs.11590
8. Find the principal which in 12 years at 5% p.a compound interest amounts to sh.450,00
. A = P (1 + R)^{n}
^{ } 100
I = A – P
A = (100 + R)^{n}
100
I = P (100 + R)^{n} – P
100
= P ( 100 + R/100)n – 1
450000 = P = 450000= 565397
9. a)Taxable income = (25000 + 12000 + 3000)= 40000
b) Income tax
10164 x ^{2}/_{20} = Shs.1016.40
10164 x ^{3}/_{20} = Shs.1524.60
10164 x ^{4}/_{20} = Shs.2032.80
Remaining :
9508 x ^{5}/_{20} = Shs.2377
Total tax payable p.m = 6950.8 – 1162 = Shs.5788.80
c) Annual tax payable = 5788.80 x 12 = Shs.69465.60
10. (a) taxable income = Kshs. 25000 + Kshs.10480
= Kshs. 35480
b) tax charged:
1^{st} 4350 = 4350 x ^{2}/_{20} = 683.25
2^{nd} 4555 = 4555 x ^{3}/_{20} – 683.25
3^{rd} 4555 = 4555 x ^{4}/_{20} – 911
4^{th} 4555 = 4555 x ^{5}/_{20} – 1138.75
Rem. 17465 = 17645 x 6/20 – 5239
Total tax – 8407.5
800.00
7607.50
(c) 40/100 x 35480 – 14.192 = 49672
New income = 35480 + 14192 = 49672
Remainder = 49672 – 18015 = 31657
Tax charged = 31657 x 6/20 =12665.1
Total tax = 12665.1
% increase in income ax = 4257.6 x 100
7607.5 = 55.97%
11. A = P(HR/100)^{n}
500000 = P( 1+ 20)^{5}
100
500,000 = (^{120}/_{100})^{5}
500,000 = P
(1.2)^{5}
P = Shs.200,938.786 shs. 200,939
12. Principal = 26, 000 – 6,000 = 20,000
Total H.P instalments = 1045.3 x 24= 25087.20
25087.20 = 20,000 1 + r
100
1.254 = 1 + r
100
1.120 = 1 + r
100
r = 0.12 or 12%
100
13. No. of periods =12
r = 4% per period
A = 1.0412 x 15000
= 24015.5
14. a) i) taxable income = 19200 + 12000 + 1300 + 2300 = 34800
b) Net tax
8400 x ^{2}/_{20} = 840
9600 x ^{3}/_{20} = 1440
12000 x ^{4}/_{20} = 2400
4800 x 5/_{20} = 1200
5800
Net tax = 5800 – 1240
= 4560
c) Net salary = 34800 – (4560 + 5530)
= 24710
15. (a) 9000 + 350 + 800 + 1200 = 11350
(b) 9000 + 3000 = 12000
(c) Total taxes = 12000 x 12
= shs.144000p.a
Taxes
450 x 2 = shs.9000
3000 x 3 = shs.9000
3000 x 4 = shs.12000
3000 x 5 = shs.15000
3000 x 6 = shs.18000
Shs.63,000
144000 – 63000= shs.81000
7y = 81000y = 11571
Taxable income= 4500 + 3000 x 4 + 11571 = K 28071p.a
Gross salary = shs. 561420p.a
(d) Total allowances = 12000 x 12
= 144,000
Basic salary = 561420
14400
Shs.417,420
Monthly basic pay = shs. 34785
16. (a) Net tax 5512
Add relief 1162
Tax payable 6674
Tax on 9680 earned
9680 X ^{10/}_{100} = 968
Tax on 9120 earned
9120 x ^{15}/ _{100} = Shs. 1368
Tax on next 9120 x ^{20}/_{100 }= Shs.1824
Tax on next 9120 x ^{25}/ _{100 }= 2280
Total 968 + 1368 + 1824 + 2280 = 6440
6674 – 6440 = 234
Let x be charged at 30%
^{30}/_{100} X x = 234
X = 234 X 100 = Shs.780
30
Total chargeable Income
780 + (9120 x 3) + 9680 = 37820
Salary 37820 – 15220 = Shs.2260 per month.
b) Net salary (37820 – 1270 – 6674) = Shs.29876
17. a) 1^{st} year after dep. Of 20%
800 000 x 80
100
= Khs. 640,000……………………………………………………
2^{nd} year after dep. of 5%
= 640000 x 95
100
= 608,000 ……………………………….
The next 3 yrs
A = P 1 – R = 608,000 ( 1 – 10) ^{3}
100 100
= 698 000 (0.9)
= Sh. 443,232 ……………………………………………………
800,000 – 443,232 = Sh. 356,768 ……………………………………………………..
(b) S.I = 3000 x ^{15}/_{100} x 2
= Sh 900 …………………………………………………
A = 3000 1 + 15
100
= 3000 1.15
= sh. 3967.50 ……………………………………………….
C.I = sh 967.50
967.50 – 900 = sh 67.50 ……………………………………….
18. (i) Taxable Income
115 x 24 800 + 12000 – 1220
100
= 28520 + 12000 – 1220
= Ksh.39,300
= K₤ 1965 p.m.
(ii) Tax due 325 x 2 = sh 650
650 x 3 = sh 1950
325 x 5 = sh 1725 ………………………..
325 x 6 = sh 1950
340 x 7.50 = sh 2250
Total tax = sh. 8825 P.m………………………
without relief
(b) (i) Total deduction
= sh (7280 + 2400 + 1200 + 2 of 24 800)……………….
100
= (7280 + 2400 + 1200 + 496) + 1220
= sh (11376 +_ 1220) = sh. 12,596 P.m …………………………………………
(ii) Net income = sh (24800 + 1200 – 12596) = sh. 24,204 P.m……………………………
19. a) Total instalments = (24 x 1250)= Shs.30000
H.P = 7200 + 30000= 37200
b) 124% = 37200
100% =
C.P = 100 x 37200
124
= 30000
c) A = 30000 (1 + ^{18}/_{100})^{2}
= 30000 (1.18)^{2} = 41772
Total interest = 41772 – 30000 = 11772
20. (a) (i) (10, 500 + 6,500) x 12 = K₤ 10,20 p.a
20
(ii) 1^{st} 1980 x 2 = Kshs. 3960
2^{nd} 1980 x 3 = Kshs 5940
3^{rd} 2480 x 5 = Kshs. 12 400
4^{th} 1480 x 7 = Kshs. 10360
5^{th} 1980 x 9 = Kshs.17 820
Last 300 x 10 = Kshs 3 000
Kshs. 53 480
PAYE = 53480 – 300 x 12
12
= Shs. 4156.70
(b) Net monthly pay
17000 – 320 + 2 x 17000
100
= 17000 – 660
= Kshs 16 340.00