Financial Mathematics Assignment - University Finance Module

This financial mathematics assignment solution addresses several key concepts in finance. It begins with calculating the immediate payment from a discounted receivable, followed by comparing simple interest investments over different time periods. The solution then explores compound interest calculations with varying interest rates and compounding frequencies, and determines the present value of a series of payments. A loan amortization schedule is presented, along with calculations of interest and principal payments. The assignment also covers equity finance, derivatives, and project evaluation using NPV and IRR methods. The document includes detailed calculations and explanations for each problem, providing a comprehensive understanding of the financial principles involved. It offers a thorough analysis of financial concepts, making it a valuable resource for students studying finance. The assignment covers a range of topics, including time value of money, investment analysis, and financial instruments. The solution also includes a detailed breakdown of financial concepts.

Running head: FINANCIAL MATHEMATICS
Financial Mathematics
Name of the Student
Name of the University
Author Note

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FINANCIAL MATHEMATICS
Table of Contents
Answer to Question 1...................................................................................................................2
Answer to Question 2...................................................................................................................5
Answer to Question 3...................................................................................................................8
Bibliography...............................................................................................................................10

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Answer to Question 1
a) Payment due to the company 50000
0
Time remaining (in months) 6
Discount p.a. 16%
Immediate payment made by discount house Payment due - (Discount
percentage * Payment Due *
6/12)
46000
0
Note: In the above case, the discount is charged on
an annual basis, but we calculate it on the basis
of 6 months as that is the time available for the
payment to become due
b) Details Formula Amount
Amount in Savings account (P) 5000
Simple Interest p.a. (r) 10%
Time invested for (in years) (T) 6
i Amount at the end of 6 years P +
((P*T*R)/100
)
8000
ii Amount initially invested for 3 years P + 6500

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((P*T*R)/100
)
The new principal becomes 6500
When this amount is reinvested, the new amount at the end of
next 3 years is
Amount P +
((P*T*R)/100
)
8450
c) Amount invested in the savings account 250
Interest rate convertible monthly for the first 3 months 18%
Interest rate convertible quarterly for the first 9 months 20%
Amount of interest for 3 months PTR/100 11.25
Amount of interest for 9 months PTR/100 9.375
Amount at the end of the end of the year Initial
Invested +
Interest
271
In the above case, the payment for the second interest is done on a quarterly basis. Hence,
the time will be taken to be (3*number of months)/12.
d) Value of a monthly payment -1000

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Interest rate p.a. convertible monthly 6%
Time period of payments (in months) 9
Compounding periods per year 12
Present Value of payments P((1-(1+r)^-n))/r $8,82
3
In the above case, the values are as follows:
P = 1000
R= 6% p.a. When converted on a monthly basis, it is 0.005.
N= Number of payment periods. In this case it is 9. The value is to be taken from the annuity
table to complete the calculation related to the same.
e) Interest Rate
1 8.0% 0.93 £ 925.93
2 7.0% 0.87 £ 808.74
3 2.5% 0.93 £ 751.00
4 4.0% 0.85 £ 641.95
5 3.0% 0.86 £ 553.75
6 5.0% 0.75 £ 413.22
7 0.0% 1.00 £ 413.22
8 3.0% 0.79 £ 326.20

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FINANCIAL MATHEMATICS
9 3.0% 0.77 £ 250.01
10 5.0% 0.61 £ 153.48
Answer to Question 2
a) i)
Particulars Formula Amount
Loan amount 120000
Time period for repayment
(in years)
5
Effective rate of interest Annual Effective rate /4 1.50%
Amount of Quarterly
payment
($6,989.49)
Total number of payments 20
In the above case the annual payments made by the entity are done on a quarterly basis.
Hence, the annual interest rate is to be converted into quarterly payments. As the loan
needs to be repaid in 5 years, the total payments made by the entity are 20.
The quarterly payments need to be equal. Hence, they are to be calculated using the
following formula:
EMI = [P x R x (1+R)^N]/[(1+R)^N-1],
Where P = 120000
R = 1.5%
N = 20.

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ii)
Payment Number Payment Principal Interest Balance
$ 120,000.00
1 ($6,989.49) ($5,189.49) $1,800.00 $ 114,810.51
2 ($6,989.49) ($5,267.33) $1,722.16 $ 109,543.18
3 ($6,989.49) ($5,346.34) $1,643.15 $ 104,196.84
4 ($6,989.49) ($5,426.54) $1,562.95 $ 98,770.30
5 ($6,989.49) ($5,507.93) $1,481.55 $ 93,262.37
6 ($6,989.49) ($5,590.55) $1,398.94 $ 87,671.82
7 ($6,989.49) ($5,674.41) $1,315.08 $ 81,997.41
8 ($6,989.49) ($5,759.53) $1,229.96 $ 76,237.88
9 ($6,989.49) ($5,845.92) $1,143.57 $ 70,391.96
10 ($6,989.49) ($5,933.61) $1,055.88 $ 64,458.35
11 ($6,989.49) ($6,022.61) $966.88 $ 58,435.74
12 ($6,989.49) ($6,112.95) $876.54 $ 52,322.79
13 ($6,989.49) ($6,204.65) $784.84 $ 46,118.14
14 ($6,989.49) ($6,297.72) $691.77 $ 39,820.42
15 ($6,989.49) ($6,392.18) $597.31 $ 33,428.24
16 ($6,989.49) ($6,488.06) $501.42 $ 26,940.18
17 ($6,989.49) ($6,585.39) $404.10 $ 20,354.79
18 ($6,989.49) ($6,684.17) $
305.32
$ 13,670.62
19 ($6,989.49) ($6,784.43) $ $ 6,886.20

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205.06
20 ($6,989.49) ($6,886.20) $
103.29
$ -
In the above case, the amortisation schedule has been prepared on the basis of the
reducing balance method. The interest is calculated on the balance remaining in the loan amount.
This interest is deducted from the EMI to calculate the principal repaid. The principal is then
reduced from the total loan amount. In this manner, the total loan amount along with the loan is
repaid in 20 Instalments.
iii) The interest portion paid on the 5th payment is calculated to be $1481.55.
iv) The total interest paid after the 15th payment is calculated to be $18270.57.
v) The amount of capital portion in the 14th payment is $6297.72.
b) i)
The shares and other types of equity-type finance are a form of capital which gives the
ownership rights to the people purchasing them. Hence, any person purchasing these shares
becomes the shareholder of a company with a right in the decision making process of the
company. Annual payments in the form of dividend are received by the shareholders in this
regard. The main risk with these investments is that the shareholders do not any receive any
payments when the company is liquidated.
ii)

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Derivatives are the instruments which have an underlying item which is traded with the help of
the derivatives. Some of these items include agricultural products and other items. The value of
the derivatives change on the basis of the changes occurring in the value of these items. The
derivatives are prone to risks like stock market risk, commodity risk, interest rate risk and credit
risk. Any changes occurring in the above items cause a risk in the change in the value of the
derivatives.
Answer to Question 3
Project R
Particulars Year 0 Year 1 Year 2 Year 3
Cash Outflows (150000) (250000) (250000)
Cash Inflows 1000000
Net Cash Flow (150000) (250000) 750000
Risk Discount Rate 20%
NPV $135,416.67
Project S
Particulars Year 0 Year 1 Year 2 Year 3
Cash Outflows (150000) -75000 -250000 -250000
Cash Inflows 1000000
Net Cash Flow (150000) (75000) (250000) 750000
NPV $39,930.56

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The NPV in the above case is calculated using the following formula:
∑CF/ (1+i)^n – Initial Investment.
Where CF is the net cash flows from the project R and Project S.
The value of “I” is 0.20. The value of n is 3. This provides the value of NPV. If it is positive,
then the project should be accepted. In the above case, project R should be accepted on the basis
of NPV as it is more.
b)
IRR of Project R 55%
IRR of Project S 27%
In the above case, the IRR should be lower. This means that the project returns the
investment at a much lower rate. Hence, project S should be accepted in case of Project R.
The IRR is calculated on the basis of the Trial and Error method where the NPV is equal
to 0. The rate at which NPV becomes equal to 0 is the IRR of the project.

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Bibliography
Brockhaus, O., 2016. Equity Derivatives and Hybrids: Markets, Models and Methods. Springer.
Kulakov, N.Y. and Kastro, A.N.B., 2017. New applications of the IRR Method in the Evaluation
of investment Projects. In IIE Annual Conference. Proceedings (pp. 464-469). Institute of
Industrial and Systems Engineers (IISE).