Financial Mathematics and Business Calculations Assignment

This document presents a comprehensive solution to a financial mathematics assignment. The assignment covers a range of topics, including converting decimals and fractions to percentages, and vice versa. It also delves into various financial calculations such as simple and compound interest, and markups. The solutions demonstrate the application of financial formulas to determine amounts invested, interest earned, and break-even points. Furthermore, the assignment explores markup calculations based on cost and retail prices, and the impact of markdowns on selling prices. The solutions provided are detailed and step-by-step, providing a thorough understanding of the financial concepts involved.

Section A
Q1
a)3.72 =372
100 = 372%
b)88.12
100 =88.12%
c)0.125
100 =0.125%
d)656.3
100 =656.3%
e)789
100=789%
Q2
a)3
7 𝑡𝑜 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 =
3
7 ∗ 100%
=42.85%=4285
100
b) 6
20 = 30%
c)13
5 = 8
5
=1.6=160%
d)1
9 = 11.11%
e)28
3 = 9.33 = 933%
Q3
a)54%=0.54
b)2.38%=0.0238
c)0.00065
d)681
4 % = 273
4 % = 68.25%
=0.6825
e)2.89%=0.0289
Q4
a)35%= 7
20
b)15.22%=761
50 =1511
50
c)156%=114
25
d)3%= 3
100

e)45%= 9
20
Q5)
a) y=3x+2, x=5
=y=5*3+2
=17
b) x=2𝑝2 − 3𝑝 + 6, 𝑝 = −2
=20
c) y=7x-5, y=2.73
x=1.104
d) 𝑦 = 𝑥 − 5𝑥2 + 3, 𝑥 = 2.304
y=-21.23
e) x=y-3x, y=5
x=5-3x
x=5
4
=1.25
Section A
Q1)
a)
i) cost price =5000
Mark up based on cost price= 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒−𝑐𝑜𝑠𝑡 𝑝𝑟𝑖𝑐𝑒
𝑐𝑜𝑠𝑡 𝑝𝑟𝑖𝑐𝑒 x100
Let selling price be X
𝑋−5000
5000 = .2
X-5000=1000
X=6000RM
ii) mark up based on retail price=𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒−𝑐𝑜𝑠𝑡 𝑝𝑟𝑖𝑐𝑒
𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 x100
=𝑋−5000
𝑋 = 0.2
X-5000=.2X
.8X=5000
X=6250RM

b)
90 shirts at RM20
10% shirts at RM15
That is 9 shirts at RM15
9x15=135
Remaining 85 shirts sold at RM20
81x20=1620RM
𝑋−1620
1620 x 100=75
X=2835
𝑌−135
135 x 100=75
Y=236.25
Total = X+Y
= 2835+236.25
=RM3071.25RM
Q2)
a)
Let X is the amount invested at 10% annum and 10000-X is the amount invested 7%
A=P(1+rt)
A = simple interested amount
P= principal amount
r= interest rate in decimals
t= number of years
Total amount after 1 years= 10820
10820 = X (1+.1x1) + (10000-X)(1+.07x1)
10820 = 1.1X + 10700 - 1.07X
10820 =0.03X + 10700
0.03X = 10820 - 10700
X = 4000RM
Amount deposited at 10% is 4000RM and amount deposited at 7% is 10000-4000=6000RM

b)
i)
A=P(1+rt)
A = simple interested amount
P= principal amount
r= interest rate in decimals
t= number of years
P =500 ,r=.12, t=1
A =500 x (1+.12x1)
= 560
Interest for 1 year =560 -500
=60RM
ii)
P=500 r= 0.12 t=5
Amount after 5 years= A=P (1+rt)
A = simple interested amount
P= principal amount
r= interest rate in decimals
t= number of years
A= 500 x (1+.12x5)
=800RM
Interest for 5 years = amount after 5 years – principal amount
=800-500
= 300RM
Q3)
Markdown percent on tv set is 10%
Retail price is RM 900
Let old selling price = X
𝑜𝑙𝑑 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒−𝑛𝑒𝑤 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒
𝑜𝑙𝑑 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 = mark down

𝑋−900
𝑋 =0.1
X-900 = 0.1X
0.9 X = 900
X=1000
WORKSHEET 2
Q1
a)
A=P(1+rt)
A = simple interested amount
P= principal amount
r= interest rate in decimals
t= number of years
P= 800RM r=0.06 t=1
Amount after 1year = 800x(1+0.06x1)
= 848RM
Amount of interest = amount after 1 year- principal amount
= 848-800
= 48 RM
b)
A=P(1+rt)
A = simple interested amount
P= principal amount
r= interest rate in decimals
t= number of years
P= 1500RM t=6 r=0.11
Amount after 6 years = 1500 x (1+0.11x6)
= 2490RM
Amount of interest= Amount after 6 years- principal amount
= 2490-1500
= 990RM

c)
A=P(1+rt)
A = simple interested amount
P= principal amount
r= interest rate in decimals
t= number of years
P=2000 r=0.14 t=7
Amount after 7 years = 2000(1+0.14x7)
=3960RM
Amount of interest = Amount after 7 years –principal amount
=3960-2000
= 1960RM
Q2)
A=P(1+rt)
A = simple interested amount
P = principal amount
r= interest rate in decimals
t= number of years
Total amount to repaid= 4000x(1+0.1x4)
=5600RM
Amount of interest repayable = total amount to paid – principal amount
= 5600-4000
= 1600RM
There fore
a) =1600RM
b) =5600RM
Q3
A=P(1+rt)
A = simple interested amount
P= principal amount

r= interest rate in decimals
t= number of years
P= 5000 t=3 A=6125 r=?
6125=5000(1+3xr)
1.225=1+3r
.225=3r
r=0.075
R=7.5%
WORKSHEET 3
Q1
a) A=𝑃(1 +𝑟
𝑛)𝑛𝑡
A = Compound interested amount
P = principal amount
r = interest rate in decimals
t = number of years
n = number of times compounding per year
P= 1000 r=0.07 n=1 t=8
A= 1000(1 +.07
1 )8𝑥1
= 1718.186RM
b) A=𝑃(1 +𝑟
𝑛)𝑛𝑡
A = Compound interested amount
P = principal amount
r = interest rate in decimals
t = number of years
n = number of times compounding per year
P=2500 r=0.09 n=2 t=10
A=2500(1 +0.09
2 )2∗10
=6029.28RM
c) A=𝑃(1 +𝑟
𝑛)𝑛𝑡
A = Compound interested amount
P = principal amount
r = interest rate in decimals
t = number of years

n = number of times compounding per year
P=42000 n=4 r=0.0775 t=8
A=42000(1 +0.0775
4 )4∗8
=57094.32RM
d) A=𝑃(1 +𝑟
𝑛)𝑛𝑡
A = Compound interested amount
P = principal amount
r = interest rate in decimals
t = number of years
n = number of times compounding per year
P=180000 r=0.09 n=12 t=6.25
A= 180000(1 +0.09
12 )12∗6.25
=315247.47RM
e) A=𝑃(1 +𝑟
𝑛)𝑛𝑡
A = Compound interested amount
P = principal amount
r = interest rate in decimals
t = number of years
n = number of times compounding per year
P=150000 r=0.12 n=365 t=3
A=150000(1 +0.12
365)365∗3
=214986.6921RM
Q2
A=𝑃(1 +𝑟
𝑛)𝑛𝑡
A = Compound interested amount
P = principal amount
r = interest rate in decimals
t = number of years
n = number of times compounding per year
A=3500 P=2000 n=2 t=5 r=?
3500 = 2000(1 +𝑟
2)2∗5
1.0575=𝑟
2 + 1
r=.115
r=11.5%

WORKSHEET 4
Q1) selling price per unit=20
Variable cost per unit= 10
Contribution margin= Selling price per unit-variable cost per unit
=20-10
=10
Q2) Variable cost per unit 18
Fixed cost =RM 20000
Revenue per unit =RM35
Break even point = 𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
𝑟𝑒𝑣𝑒𝑛𝑢𝑒 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡−𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑐𝑜𝑠𝑡
=20000
35−18
=RM1176.4705