Financial Calculations and Analysis Assignment - Semester 1

This finance assignment presents solutions to various financial calculations, including formula-based problems, percentage calculations, and annuity computations. Task 1 focuses on solving mathematical formulas. Task 2 involves percentage and fraction conversions, and calculating percentage changes. Task 3 delves into compound interest, loan and annuity calculations, and future value determinations. Task 4 analyzes break-even points, exploring fixed costs, variable costs, and sales revenues to determine the break-even unit and amount. Finally, Task 5 analyzes employee data to determine the number of employees with leave greater than 10 days and training less than 3 days. The assignment includes references to relevant financial literature.

USING AND MANAGING
DATA AND INFORMATION

TABLE OF CONTENTS
TABLE OF CONTENTS................................................................................................................2
TASK 1............................................................................................................................................1
TASK 2............................................................................................................................................1
TASK 3............................................................................................................................................2
TASK 4............................................................................................................................................4
TASK 5............................................................................................................................................5
REFERENCES................................................................................................................................6

TASK 1
a
21.2 -16.8 x 0.67
Formula = (21.2-16.8)*0.67
2.948
b
5.48 + 3.8 x 1.9 /√27
Formula = (5.48 + 3.8)*( 1.9/SQRT(27))
3.393
c
(369 – 173 / 4) ÷ 68 / √83
Formula = ((369-173)/4)/(68/SQRT(83))
6.565
d
(2864 – (143 x 36)/32 ) ÷ √2568 − 121/4 x √630 − 5(89)
Formula = (2864-(143*36)/(3^2))/SQRT(2568-(121/4))*(SQRT(630-
(5*89))
618.84
e
(34.78 – (5.63)^2 ) ÷ ( √365) / 5^2
Formula = (34.78-(5.63^2))/(SQRT(365)/5^2)
4.034
TASK 2
a
46.70%
Fraction 0.467
Formula 46.7/100
b
1

0.01896
Percentage 1.90%
Formula 0.01896*100
c
0.7777
x= 0.7777
10x = 7.7777
x(10-1) = 7
x = 7/9
Fraction 7/9
d
51/63
Formula (51/63)*100
80.95238095
e
Year
2018 166
2019 189
Change (189-166)/166
13.86%
TASK 3
a
Principal 20000
Interest rate 5%
Maturity 5 years
Formula P(1+i)^n
20000*((1+0.05)^5)
Amount earned 25525.63125
2

b
Loan amount 300000
Annuity Payment P=[( r * PV/1-(1+r)^n]
[(300000 * 0.035) / 1 - (1.035)^5]
66445
OR
Annuity Factor (1+i)^n
4.515
Annual premiums A / (1+I)^n
300000/4.5150
Annual premiums 66445.18272
c
Monthly Installment
P 800
r 2.25 / 12 = 0.280333
n 5*12 = 60
Future value of
annuity P[(1+r)^n-1/r]
FV 800*[(1+0.0020833)^60 - 1/0.0028333]
Monthly Installment 51067.31
d
Monthly Repayments
Loan (P) 45000
Interest 6 /12 =0.5%
PV of annuity P=[( r * PV/1-(1+r)^n]
[(45000 * 0.005) / 1 - (1.005)^60]
Monthly Repayments 869.98
3

e
Future Value 50000
Interest rate 4%
FV FV/(1+r)^n
50000/(1.04)^6
42740.21
TASK 4
Break Even
Break Even
Fixed Cost
Selling price -
Variable Cost
Fixed Cost 5200
Variable cost 1.25
Selling price 4.5
Break even (units) 5200 / (4.5 -1.25)
1600
Sales units
Sales
revenues @
4.5 Cost
Contributio
n margin
Break Even
(amount)
0 0 0
200 900 250 27.78% 18720
400 1800 500 27.78% 18720
600 2700 750 27.78% 18720
800 3600 1000 27.78% 18720
1000 4500 1250 27.78% 18720
1200 5400 1500 27.78% 18720
1400 6300 1750 27.78% 18720
1600 7200 2000 27.78% 18720
1800 8100 2250 27.78% 18720
2000 9000 2500 27.78% 18720
4

TASK 5
A B C
Employee
Holidays taken
(days)
Training completed
(days)
Leave >10 days
& Training <3
days
1 6 4 No
2 10 2 No
3 12 1 Yes
4 7 1 No
5 8 3 No
6 11 2 Yes
7 9 4 No
8 6 3 No
9 8 1 No
10 11 2 Yes
11 13 1 Yes
12 8 4 No
13 12 3 No
14 6 1 No
15 13 2 Yes
16 8 2 No
17 10 3 No
18 11 4 No
19 8 2 No
20 9 2 No
21 7 4 No
22 12 1 Yes
23 11 2 Yes
24 6 1 No
25 14 3 No
Employees with leave > 10 10
Employees completed < 2
training days 7
5

REFERENCES
Books and Journals
Ryser, H.J., 2018. Combinatorial mathematics (Vol. 14). American Mathematical Soc..
Marsden, S.A.J., and et.al., 2019. Interdisciplinary Applied Mathematics.
Frees, E.W., Carriere, J. and Valdez, E., 2016. Annuity valuation with dependent
mortality. Journal of Risk and Insurance. pp.229-261.
Midlam, M., Asset Marketing Systems Insurance Services LLC, 2017. Indexed annuity system
and method. U.S. Patent Application 10/981,214.
Atkinson, L., and et.al., GENWORTH FINANCIAL Inc, 2018. System and method for cross
funding of multiple annuity contracts. U.S. Patent Application 10/294,820.
Ekren, O., Ekren, B.Y. and Ozerdem, B., 2019. Break-even analysis and size optimization of a
PV/wind hybrid energy conversion system with battery storage–A case study. Applied
Energy. 86(7-8). pp.1043-1054.
Online
Annuities. 2019. [Online]. Available through :
< https://worldscientific.com/doi/pdf/10.1142/9789813224681_0002>.
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