BEA140 Quantitative Methods: Financial Maths Assignment Semester 2

This document presents a detailed solution to a Quantitative Methods & Financial Maths assignment, addressing key concepts such as loan repayment schedules, effective interest rates, and bond valuation. The assignment involves calculating monthly payments for a loan, constructing a loan repayment schedule, and determining the impact of interest rates. It further explores investment strategies, including sinking funds, to achieve financial goals. The solution provides step-by-step calculations and explanations, offering a comprehensive understanding of the financial principles involved. Desklib offers a range of solved assignments and study materials to aid students in their academic pursuits.

Running head: QUANTITATIVE METHODS & FINANCIAL MATHS
Quantitative Methods & Financial Maths
Name of the Student:
Name of the University:
Author’s Note:

1QUANTITATIVE METHODS & FINANCIAL MATHS
Table of Contents
Answer to Question 1:.....................................................................................................................2
Requirement a:.............................................................................................................................2
Requirement b:.............................................................................................................................2
Requirement c:.............................................................................................................................3
Requirement d:.............................................................................................................................4
Requirement e:.............................................................................................................................6
Answer to Question 2:.....................................................................................................................7
Requirement a:.............................................................................................................................7
Requirement b:.............................................................................................................................7
Requirement c:.............................................................................................................................8
Requirement d:.............................................................................................................................8
Requirement e:.............................................................................................................................9
Bibliography:.................................................................................................................................10

2QUANTITATIVE METHODS & FINANCIAL MATHS
Answer to Question 1:
Requirement a:
Total Amount to be Repaid:
Particulars Amount
Amount Borrowed $1,80,000.00
Rate of Loan Establishment Fees 0.35%
Loan Establishment Fees $630
Total Amount to be Repaid $1,80,630.00
Time-Line Diagram:
Period 0 Period 96Period 2
$2,352.68
Monthly Payment
Period 3
$2,352.68
Monthly Payment
Loan Taken
$1,80,000.00
$2,352.68
Monthly Payment
Period 1 Period 95
$2,352.68 $2,352.68
Monthly Payment Monthly Payment
Requirement b:
Particulars Amount
Total Amount to be Repaid $1,80,630.00
Repayment Period (in yrs.) 8
Nos. of Payments p.a. 12
Total Nos. of Payments 96
Interest Rate p.a. 5.76%
Interest Rate p.m. 0.48%
Size of Regular Payments $2,352.68

3QUANTITATIVE METHODS & FINANCIAL MATHS
The total loan, amounted to $ 1,80,630, has to be repaid with 96 nos. of equal monthly
payments, i.e., within 8 years, and the interest on the loan has to be paid at the rate 5.76% per
annum. Therefore, the total interest on the loan would be ($1,80,630 x 5.76% x 8) $83,234.30
and the total repayment amount, including the interest, would be ($1,80,630.00 + $83,234,30)
$2,63,864.30. If this total amount has to be paid by 96 nos. of equal payments, then the size of
equal payments would be ($2,63,864.30 / 96) $2,748.59. As per the calculations above, the size
of the regular payments would be $ 2,352.68. The difference between the two amounts is near
about $300 and it is caused due to the decrease of principal amount with every regular payment.
Therefore, it can be stated that the amount, derived in the table above, is proper.
Requirement c:
Particulars Rate 1 Rate 2 Rate 3
Comparison
Rate 1 Rate 5 Rate 6
Comparison
Rate 2
Total Amount to be Repaid $1,80,630.00 $1,80,631.00 $1,80,632.00 $1,80,633.00 $1,80,629.00 $1,80,628.00 $1,80,627.00
Repayment Period (in yrs.) 8 8 8 8 8 8 8
Nos. of Payments p.a. 12 12 12 12 12 12 12
Total Nos. of Payments 96 96 96 96 96 96 96
Size of Regular Payments $2,352.68 $2,352.68 $2,352.68 $2,352.68 $2,352.68 $2,352.68 $2,352.68
Interest Rate p.a. 5.7600% 5.7599% 5.7597% 5.7596% 5.7601% 5.7603% 5.7604%
Effective Interest Rate 5.9141% 5.9150%

4QUANTITATIVE METHODS & FINANCIAL MATHS
Requirement d:
Period Op. Balance
Monthly
Payment Interest Rate Interest Paid Principal Paid Cl. Balance
1 $1,80,630.00 $2,352.68 5.76% $867.02 $1,485.66 $1,79,144.34
2 $1,79,144.34 $2,352.68 5.76% $859.89 $1,492.79 $1,77,651.55
3 $1,77,651.55 $2,352.68 5.76% $852.73 $1,499.96 $1,76,151.59
4 $1,76,151.59 $2,352.68 5.76% $845.53 $1,507.16 $1,74,644.43
5 $1,74,644.43 $2,352.68 5.76% $838.29 $1,514.39 $1,73,130.04
6 $1,73,130.04 $2,352.68 5.76% $831.02 $1,521.66 $1,71,608.38
7 $1,71,608.38 $2,352.68 5.76% $823.72 $1,528.96 $1,70,079.42
8 $1,70,079.42 $2,352.68 5.76% $816.38 $1,536.30 $1,68,543.12
9 $1,68,543.12 $2,352.68 5.76% $809.01 $1,543.68 $1,66,999.44
10 $1,66,999.44 $2,352.68 5.76% $801.60 $1,551.09 $1,65,448.35
11 $1,65,448.35 $2,352.68 5.76% $794.15 $1,558.53 $1,63,889.82
12 $1,63,889.82 $2,352.68 5.76% $786.67 $1,566.01 $1,62,323.81
13 $1,62,323.81 $2,352.68 5.76% $779.15 $1,573.53 $1,60,750.28
14 $1,60,750.28 $2,352.68 5.76% $771.60 $1,581.08 $1,59,169.19
15 $1,59,169.19 $2,352.68 5.76% $764.01 $1,588.67 $1,57,580.52
16 $1,57,580.52 $2,352.68 5.76% $756.39 $1,596.30 $1,55,984.22
17 $1,55,984.22 $2,352.68 5.76% $748.72 $1,603.96 $1,54,380.26
18 $1,54,380.26 $2,352.68 5.76% $741.03 $1,611.66 $1,52,768.60
19 $1,52,768.60 $2,352.68 5.76% $733.29 $1,619.40 $1,51,149.21
20 $1,51,149.21 $2,352.68 5.76% $725.52 $1,627.17 $1,49,522.04
21 $1,49,522.04 $2,352.68 5.76% $717.71 $1,634.98 $1,47,887.06
22 $1,47,887.06 $2,352.68 5.76% $709.86 $1,642.83 $1,46,244.24
23 $1,46,244.24 $2,352.68 5.76% $701.97 $1,650.71 $1,44,593.52
24 $1,44,593.52 $2,352.68 5.76% $694.05 $1,658.64 $1,42,934.89
25 $1,42,934.89 $2,352.68 5.76% $686.09 $1,666.60 $1,41,268.29
26 $1,41,268.29 $2,352.68 5.76% $678.09 $1,674.60 $1,39,593.70
27 $1,39,593.70 $2,352.68 5.76% $670.05 $1,682.63 $1,37,911.06
28 $1,37,911.06 $2,352.68 5.76% $661.97 $1,690.71 $1,36,220.35
29 $1,36,220.35 $2,352.68 5.76% $653.86 $1,698.83 $1,34,521.52
30 $1,34,521.52 $2,352.68 5.76% $645.70 $1,706.98 $1,32,814.54
31 $1,32,814.54 $2,352.68 5.76% $637.51 $1,715.17 $1,31,099.37
32 $1,31,099.37 $2,352.68 5.76% $629.28 $1,723.41 $1,29,375.96
33 $1,29,375.96 $2,352.68 5.76% $621.00 $1,731.68 $1,27,644.28
34 $1,27,644.28 $2,352.68 5.76% $612.69 $1,739.99 $1,25,904.29
35 $1,25,904.29 $2,352.68 5.76% $604.34 $1,748.34 $1,24,155.94
36 $1,24,155.94 $2,352.68 5.76% $595.95 $1,756.74 $1,22,399.21
37 $1,22,399.21 $2,352.68 5.76% $587.52 $1,765.17 $1,20,634.04
38 $1,20,634.04 $2,352.68 5.76% $579.04 $1,773.64 $1,18,860.40
39 $1,18,860.40 $2,352.68 5.76% $570.53 $1,782.15 $1,17,078.25
40 $1,17,078.25 $2,352.68 5.76% $561.98 $1,790.71 $1,15,287.54
Loan Repayment Schedule:

5QUANTITATIVE METHODS & FINANCIAL MATHS
41 $1,15,287.54 $2,352.68 5.76% $553.38 $1,799.30 $1,13,488.23
42 $1,13,488.23 $2,352.68 5.76% $544.74 $1,807.94 $1,11,680.29
43 $1,11,680.29 $2,352.68 5.76% $536.07 $1,816.62 $1,09,863.67
44 $1,09,863.67 $2,352.68 5.76% $527.35 $1,825.34 $1,08,038.33
45 $1,08,038.33 $2,352.68 5.76% $518.58 $1,834.10 $1,06,204.23
46 $1,06,204.23 $2,352.68 5.76% $509.78 $1,842.90 $1,04,361.33
47 $1,04,361.33 $2,352.68 5.76% $500.93 $1,851.75 $1,02,509.58
48 $1,02,509.58 $2,352.68 5.76% $492.05 $1,860.64 $1,00,648.94
49 $1,00,648.94 $2,352.68 5.76% $483.11 $1,869.57 $98,779.37
50 $98,779.37 $2,352.68 5.76% $474.14 $1,878.54 $96,900.83
51 $96,900.83 $2,352.68 5.76% $465.12 $1,887.56 $95,013.27
52 $95,013.27 $2,352.68 5.76% $456.06 $1,896.62 $93,116.65
53 $93,116.65 $2,352.68 5.76% $446.96 $1,905.72 $91,210.92
54 $91,210.92 $2,352.68 5.76% $437.81 $1,914.87 $89,296.05
55 $89,296.05 $2,352.68 5.76% $428.62 $1,924.06 $87,371.99
56 $87,371.99 $2,352.68 5.76% $419.39 $1,933.30 $85,438.69
57 $85,438.69 $2,352.68 5.76% $410.11 $1,942.58 $83,496.11
58 $83,496.11 $2,352.68 5.76% $400.78 $1,951.90 $81,544.21
59 $81,544.21 $2,352.68 5.76% $391.41 $1,961.27 $79,582.94
60 $79,582.94 $2,352.68 5.76% $382.00 $1,970.69 $77,612.25
61 $77,612.25 $2,352.68 5.76% $372.54 $1,980.15 $75,632.10
62 $75,632.10 $2,352.68 5.76% $363.03 $1,989.65 $73,642.45
63 $73,642.45 $2,352.68 5.76% $353.48 $1,999.20 $71,643.25
64 $71,643.25 $2,352.68 5.76% $343.89 $2,008.80 $69,634.46
65 $69,634.46 $2,352.68 5.76% $334.25 $2,018.44 $67,616.02
66 $67,616.02 $2,352.68 5.76% $324.56 $2,028.13 $65,587.89
67 $65,587.89 $2,352.68 5.76% $314.82 $2,037.86 $63,550.03
68 $63,550.03 $2,352.68 5.76% $305.04 $2,047.64 $61,502.38
69 $61,502.38 $2,352.68 5.76% $295.21 $2,057.47 $59,444.91
70 $59,444.91 $2,352.68 5.76% $285.34 $2,067.35 $57,377.56
71 $57,377.56 $2,352.68 5.76% $275.41 $2,077.27 $55,300.29
72 $55,300.29 $2,352.68 5.76% $265.44 $2,087.24 $53,213.05
73 $53,213.05 $2,352.68 5.76% $255.42 $2,097.26 $51,115.79
74 $51,115.79 $2,352.68 5.76% $245.36 $2,107.33 $49,008.46
75 $49,008.46 $2,352.68 5.76% $235.24 $2,117.44 $46,891.01
76 $46,891.01 $2,352.68 5.76% $225.08 $2,127.61 $44,763.41
77 $44,763.41 $2,352.68 5.76% $214.86 $2,137.82 $42,625.59
78 $42,625.59 $2,352.68 5.76% $204.60 $2,148.08 $40,477.50
79 $40,477.50 $2,352.68 5.76% $194.29 $2,158.39 $38,319.11
80 $38,319.11 $2,352.68 5.76% $183.93 $2,168.75 $36,150.36

6QUANTITATIVE METHODS & FINANCIAL MATHS
Nos. of Payments:
Particulars Amount
Balance Loan Payment $36,150.36
Interest Rate p.a. 5.37%
Nos. of Payments p.a. 12
Interest Rate p.m. 0.448%
Monthly Payments $2,352.68
Total Nos. of Payments required 15.95
Requirement e:
Particulars Amount
Monthly Payment $2,352.68
Total Nos. of Payments required 15.95
Final Partial Payment $2,246.78
The loan balance due after 80th instalment would be $36,150.36 and the amount of
monthly payment would be $2,352.68. For the next 15 nos. of instalment periods, if interest
would be charged on the due principal amount at the rate 0.448% per month, then the total
interest due would be ($36,150.36 x 0.448% x 15) $2,426.59 and the total amount due would be
($36,150.36 + $2,426.59) $38,576.95. The total amount paid after in the next 15th instalment
would be ($2,352.62 x 15) $35,290.26 and the final partial payment would be then ($38,576.95 -
$35,290.26) $3,286.69. However, as with each monthly payment, the principal amount would
decrease, the actual total interest amount would be lower than $2,426.59. As the result, the actual
final partial payment would also be lower than $3,286.69 and hence, the final partial payment,
calculated in the table above, is correct.

7QUANTITATIVE METHODS & FINANCIAL MATHS
Answer to Question 2:
Requirement a:
Particulars Amount
Face Value $5,000.00
Coupon Rate 10%
Nos. of Coupon Payment p.a. 2
Maturity Period 4
Size of Each Coupon Dividends $250.00
Final Maturity Dividend $5,250.00
$250
Cash Inflow
$0
Cash Inflow
$250
Cash Inflow Cash Inflow
$250
Period 3
Cash Inflow
$250
Period 4
Cash Inflow
$250
Period 5
Cash Inflow
$250
Period 6
Cash Inflow
$250
Period 7
Cash Inflow
$5,250
Period 0 Period 8Period 2Period 1
Requirement b:
Particulars Amount
Coupon Dividend $250.00
Nos. of Deposit p.a. 2
Total Period (in years) 4
Total Nos. of Deposit 8
Interest Rate p.a. 6.10%
Half-Yearly Interest Rate 3.05%
Total Deposit Value $2,227.03
Face Value $5,000.00
Accumulated Amount in
Investment Account $7,227.03

8QUANTITATIVE METHODS & FINANCIAL MATHS
Requirement c:
Cash Inflow Cash Inflow Cash Inflow Cash Inflow Cash Inflow Cash Inflow Cash Inflow Cash Inflow
Period 5
Cash Inflow
$0 $392 $392 $392 $392 $392 $392 $392 $392
Period 0 Period 1 Period 2 Period 3 Period 4 Period 6 Period 7 Period 8
Cash Inflow
$392
Period 9
Cash Inflow
$392
Period 12
Cash Inflow
$392
Period 10
Cash Inflow
$392
Period 11
Requirement d:
Particulars Amount
Required Fund $20,000.00
Total Period (in years) 10
1st Deposit (in Years) 0.5
Nos. of Half Yearly Deposits 12
Last Period of Deposit (in years) 6.5
Balance Periods (in years) 3.5
Interest Rate p.a. 6.10%
Value of Deposit after 6.5 yrs. $16,256.47
Initial Investment Amount $7,227.03
Interest in first six months $220.42
Investment value after 6 months $7,447.46
Size of Regular Deposit,R $391.79

9QUANTITATIVE METHODS & FINANCIAL MATHS
Requirement e:
Investment Value after 9 Deposits:
Particulars Amount
Investment Value after six months $7,447.46
Total Nos. of Half Yearly Deposits 12
Deposits Due 3
Nos. of Deposits made 9
Size of Regular Deposits,R $391.79
Interest Rate p.a. 6.10%
Investment Value after 5 yrs. $13,748.16
Sinking Fund Table:
Period
Op.
Balance
Intrest
Rate
Interest
Amount Deposit Cl. Balance
5.5 $13,748.16 6.10% $419.32 $391.79 $14,559.27
6 $14,559.27 6.10% $444.06 $391.79 $15,395.12
6.5 $15,395.12 6.10% $469.55 $391.79 $16,256.47

10QUANTITATIVE METHODS & FINANCIAL MATHS
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