Uploaded by Jess Lee Pui Sze

Maths (Repaired)

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ASSIGNMENT QUESTIONS
1. Khairul needs to do 13 payments for an investment. The fourth payment divided by the
second payment equals to 4. If the last payment is RM8,192, and the common ratio is
positive, compute the:
a) common ratio
T4
4
=
T2
,
1
T13 =8192
T2 = ar1 = 1------- 1
T4 = ar3 = 4------- 2
ar1
2÷1
ar3
4
=1
r3-1=4
r2=4
r=√4
r=2
[3m]
b) first payment
T2=ar1=1-----1
r=2----------2
Substitute 2 into 1
a (21) =1
1
a=2
[3m]
c) sum of all the payment.
1
2
(2n-1) =8192
S15= a(rn-1)
2n-1=16384
log2n-1=log16384
(n-1) log2=log16384
n-1=14
(r-1)
1
= 2(215-1)
2-1
=16383.5
[2m]
2. Ahmad and his wife have four children. The eldest is studying in local university doing
their bachelor degree while the rest are still schooling. Their income and expenses are as
follows:
Income and Expenses
Ahmad (RM)
Wife (RM)
Income
60,000
36,000
EPF
6,600
3,960
LIP
1,800
1,200
300
200
3,500
1,500
1,000
-
500
300
Cash contribution
Medical expenses for
parents
Book and Journal
Zakat
Calculate their tax payable if they choose:
a) joint assessment
[14m]
Income
RM9600
Less Deductions:
RM
1.Personal
9000
2.Wife
3000
3.Children
9000
4.EPF&LIP
6000
5.Cash Contribution
500
6.Medical expenses for
3500
parents
1000
7.Book and Journal
(32000)
Chargeable Income
64000
Tax assessment
Rate
Tax
On the first RM50000
-
2850
On the next RM14000
19%
2660
Tax amount
5510
Less Zakat
-800
Tax payable
4710
b) separate assessment
[26m]
Ahmad
Income
RM60,000
Less Deductions:
RM
1.Personal
9000
2.Children
9000
3.EPF&LIP
6000
4.Cash Contribution
300
5.Medical expenses for
3500
parents
6.Book and Journal
1000
31200
Chargeable Income
Tax assessment
(28800)
Rate
Tax
On the first RM20000
-
300
On the next RM11200
6%
672
Tax amount
972
Less tax rebates
-400
572
Less Zakat
Tax payable
-500
72
Ahmad‡s wife
Income
RM36000
Less Deductions:
RM
1.Personal
9000
2.EPF&LIP
5160
3.Cash Contribution
200
4.Medical expenses for
1500
parents
(15860)
20140
Chargeable Income
Tax assessment
On the first RM20000
On the next RM140
Rate
Tax
-
300
6%
8.4
Tax amount
308.4
Less tax rebates
-400
-91.60
Less Zakat
Tax payable
300
-391.60
3. Jason would like to receive an annuity of RM5,000 semiannually for 10 years after he
retires. He will retire in 18 years. Money is worth 6%, compounded semiannually.
a) Calculate the amount of money Jason would have when he retires in order to finance
this annuity.
𝑖=
Payment = RM5000
K=2
R = 6%
T =10 years
𝑅
𝐾
n =kt
= 0.06
=2(10)
2
= 20
= 0.03
FV = π‘π‘šπ‘‘ × (1+ 𝑖)n-1
𝑖
= RM5000 × (1+0.03)20-1
0.03
= RM134351.87
[5m]
b) Determine the single deposit made now that would provide the funds for the annuity.
PV = 𝐹𝑉
(1+ 𝑖)n
= 134351.87
(1+0.03)20
=RM 74387.37
[5m]
c) Compute the amount that Jason will actually receive in payments from the annuity.
M = P( 1+ 𝑖)n
= RM5000(1+0.03)20
= RM9030.56
[2m]
d) Compute the interest that the single deposit earns before the annuity ends.
I = A – (n - 𝑃𝑀𝑇)
=RM 134351.87 – ( 20 × RM5000)
=RM34351.87
[2m]
4. Create an invoice for 6 items which are related to the company you have suggested.
Compute the total invoice amount that you have created if the trade discount is 5/10, cash
discount is 20/15, 10/25, n/60 and the invoice was paid on the 20th day of the invoice date.
Include the shipping and insurance amount of RM 50 into the invoice. More marks will be
given for creativity of the invoice.
[18m]
Invoice was paid on 20th day
Invoice No: 95-961
Date: September 8
Terms:20/15,10/25,n/60
Quantity
Description
Unit List Price
Total
6
Jacket&Coats Men
RM32.90 each
RM197.40
8
Hoodies&Sweatshirts
RM31 each
RM248
12
Pants Leggings
RM23.60 each
RM283.20
Women
5
Sneakers Women
RM27.20 each
RM136
10
T-shirts Men’s
RM24 each
RM240
4
Dresses
RM19 each
RM76
Total list price
RM1180.60
Trade Discount 5/10
RM171.19
Total after trade
RM1009.41
discount
Cash Discount
RM201.88
Net Cost
RM807.53
Shipping and
RM50
Insurance
Total Invoice
Amount
RM875.53
5. Radzi wants to sell his car, which was purchased for RM100,000, after using it for four
years. The residual value after eight years is estimated to be RM20,000. Two second-hand
dealers are offering to sell her car based on the book value. Agency Cool Car is using the
declining method while Agency Fresh Car is using the sum of year digits method to
calculate the depreciation.
a) Construct the depreciation schedule for the first 5 years for Agency Cool Air using the
declining balance method.
Declining Balance Method
Cost = RM100,000
Salvage Value = RM20,000
Useful Life = 8 years
8
20,000
Annual depreciation r= 1 - √100,000
= 0.1822
Year
Ann .Dep
Acc. Dep
BV
0
-
-
RM100,000
1
0.1822×100,000
RM18220
=RM81,780
=RM18220
2
3
4
5
100,000-18220
0.1822×81780
18220+14900.32
81,780-18220
=RM14900.32
=RM33120.32
=RM66,879.68
0.1822×66,879.68
33120.32+12185.40
66,879.68-18220
=RM12,185.48
=RM45305.80
=RM54,694.20
0.1822×54,594.20
45305.80+9965.28
54,694.20-18220
=RM9965.28
=RM55,271.08
=RM44,728.92
0.1822×44,728.92
55,271.08+8149.61
44,728.92-18220
=RM8149.61
=RM63,420.69
=RM36,579.31
[7m]
b) Construct the depreciation schedule for the first 5 years for Agency Fresh Car using
sum-of-year digits method.
Sum of Year Digits Method
Cost = RM100,000
Salvage Value = RM20,000
Total depreciation = cost- salvage value
=RM100,000 – RM20,000
=RM 80,000
Useful Life = 8 years
Sum of Days = n(n+1)
2
= 8(8+1)
2
= 36
Year
Fraction
Ann.Dep
Acc.Dep
BV
0
-
-
-
RM100,000
1
8/36
RM17,777.78
RM82,222.22
RM33,333.34
RM66,666.66
RM46,666.67
RM53,333.33
RM57,777.78
RM42,222.22
RM66,666.68
RM33,333,32
8/36×80,000
=RM17777,78
2
7/36
7/36×80,000
=RM15555.56
3
6/36
6/36×80,000
=RM13333.33
4
5/36
5/36×80,000
=RM11111.11
5
4/36
4/36×80,000
=RM8888.90
[10m]
c) Identify which car dealer is offering a better deal to Radzi. State your reason.
Agency Fresh Car is a better deal to Radzi.This is because Agency Fresh Car is more
cheaper than Agecy Cool Car.
[3m]
END OF PAGE
FACULTY OF BUSINESS & MANAGEMENT (FBM)
DBM1102 BUSINESS MATHEMATICS
ACADEMIC SESSION
SEMESTER: JULY 2019
LECTURER’S NAME: Azzuana Fakhrinie Binti Ramli
SUBMISSION DATE:23/9/2019
PREPARED BY
NAME: LEE PUI SZE
MATRIC ID NO.: QIUP-201907-003253