Financial Mathematics, business and finance assignment help

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User Generated

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Perfgre

Subject

Business Finance

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This documents consist of two financial mathematics questions, which require the use of Python 2.7.10.0 (a screenshot will be suffice) and Excel to calculate the following questions.

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Question 1 (a) Using Python in your calculations, do the following exercises (i), (ii) and (iii). (i) You invest $83 now and receive back a total of $83.64 after 28 days. What is the yield on your investment? (ii) You receive 6.5% per annum on a 138-day deposit. What is the effective rate? What is the daily equivalent rate? What is the 138-day discount factor? (iii) What is the NPV of the following cashflows using an effective annual interest rate of 10% per annum? Now: 6 months: 12 months: 18 months: 24 months: 36 months: (b) -$105 -$47 -$47 -$47 -$47 +$450 Use Excel to do this question. It is 1 January 2017 and Mary has just bought a condominium for $2 million. She has succeeded in securing a loan of 70% of the purchase price, payable over 30 years. She will start paying the instalments at the end of the month. The interest rate is 1.6% per annum. (i) Compute the monthly instalment she has to pay. (ii) Calculate the outstanding principal balance at the end of one year. (iii) Draw up a table showing the month-by-month instalments broken down into interest paid, principal repaid, and principal outstanding at the end of each month. Question 2 (a) Using Python, do the following exercises (i) and (ii). (i) What are the weighted arithmetic and geometric means of the following numbers, given the following weightings? 12 (weighting 11%) 7 (weighting 19%) 13 (weighting 7%) 1 10 15 4 (ii) (weighting 23%) (weighting 16%) (weighting 3%) (weighting 21%) What is the volatility of the portfolio consisting of the following two assets? Current value A: B: 2 million 3 million Volatility 8.1% 15.4% Correlation between A and B: + 0.37 (b) Anna is a novice stock investor, having just graduated from the University. She has one stock, X, in her portfolio currently and is looking to build a portfolio of stocks. She is considering adding one more stock into her portfolio and is examining three possible stocks, A, B and C. These 3 stocks have identical characteristics and she is indifferent between the three stocks. She has found the following data on these three stocks: Covariance between X and stock A = 0.72 Variance of X = 0.64 Variance of A = 0.81 Covariance between X and stock B = 0 Variance of X = 0.64 Variance of B = 0.30 Covariance between X and stock C = -0.40 Variance of X = 0.64 Variance of C = 0.25 and X and C are negatively correlated. Apply the relevant formula to compute the portfolio risk in each of these cases, using appropriate values where available from the question. Which stock should she choose? Explain your choice.
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(i) Initial Value
Ending Value
Holding Period Yield
(i) Annual Rate
Total Days
Effective Interest Rate
Daily Equivalent Rate
138 Days Discount Factor

$
$

83,00
83,64
0,77%
6,50%
138
6,71%
0,018%
0,9765

(iii)
Particulars
Cash Flows
Discount Factor (10%)
Discounted Value
Net Presenet Value (NPV)

Now
(105,00)
1,0000
(105,00)
65,97

NPV Calculation
6 Month
12 Month
(47,00)
(47,00)
0,9535
0,9091
(44,81)
(42,73)

18 Month
(47,00)
0,8668
(40,74)

24 Month
(47,00)
0,8264
(38,84)

36 Month
450,00
0,7513
338,09

(a) Monthly Installment

$4.899,15

(b) Outstanding principal balance at the
$1.363.342,19
end of one year
(c) Mortgage Amortization Table
Mortgage
Principle Value
Annual
Interest Rate

Month
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

$1.400.000
1,60%

Beginning
Balance
$1.400.000,00
$1.396.967,52
$1.393.931,00
$1.390.890,42
$1.387.845,80
$1.384.797,11
$1.381.744,36
$1.378.687,54
$1.375.626,65
$1.372.561,67
$1.369.492,60
$1.366.419,45
$1.363.342,19
$1.360.260,84
$1.357.175,37
$1.354.085,79
$1.350.992,09
$1.347.894,27
$1.344.792,31
$1.341.686,22
$1.338.575,99
$1.335.461,61
$1.332.343,08
$1.329.220,39
$1.326.093,54
$1.322.962,52
$1.319.827,32
$1.316.687,95
$1.313.544,38
$1.310.396,63

Mortgage Term
(Months)
Monthly
Payment (PMT)

360
$4.899,15

Mortgage Amortization Table
Monthly
Periodic Interest Periodic Principal
Payment
Paid
Repaid
$4.899,15
$1.866,67
$3.032,48
$4.899,15
$1.862,62
$3.036,52
$4.899,15
$1.858,57
$3.040,57
$4.899,15
$1.854,52
$3.044,63
$4.899,15
$1.850,46
$3.048,69
$4.899,15
$1.846,40
$3.052,75
$4.899,15
$1.842,33
$3.056,82
$4.899,15
$1.838,25
$3.060,90
$4.899,15
$1.834,17
$3.064,98
$4.899,15
$1.830,08
$3.069,06
$4.899,15
$1.825,99
$3.073,16
$4.899,15
$1.821,89
$3.077,25
$4.899,15
$1.817,79
$3.081,36
$4.899,15
$1.813,68
$3.085,47
$4.899,15
$1.809,57
$3.089,58
$4.899,15
$1.805,45
$3.093,70
$4.899,15
$1.801,32
$3.097,82
$4.899,15
$1.797,19
$3.101,95
$4.899,15
$1.793,06
$3.106,09
$4.899,15
$1.788,91
$3.110,23
$4.899,15
$1.784,77
$3.114,38
$4.899,15
$1.780,62
$3.118,53
$4.899,15
$1.776,46
$3.122,69
$4.899,15
$1.772,29
$3.126,85
$4.899,15
$1.768,12
$3.131,02
$4.899,15
$1.763,95
$3.135,20
$4.899,15
$1.759,77
$3.139,38
$4.899,15
$1.755,58
$3.143,56
$4.899,15
$1.751,39
$3.147,75
$4.899,15
$1.747,20
$3.151,95

31
32
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35
36
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46
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57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77

$1.307.244,68
$1.304.088,52
$1.300.928,16
$1.297.763,59
$1.294.594,79
$1.291.421,77
$1.288.244,52
$1.285.063,03
$1.281.877,30
$1.278.687,33
$1.275.493,10
$1.272.294,61
$1.269.091,85
$1.265.884,83
$1.262.673,53
$1.259.457,95
$1.256.238,08
$1.253.013,92
$1.249.785,45
$1.246.552,69
$1.243.315,61
$1.240.074,22
$1.236.828,51
$1.233.578,46
$1.230.324,09
$1.227.065,37
$1.223.802,31
$1.220.534,90
$1.217.263,14
$1.213.987,01
$1.210.706,51
$1.207.421,64
$1.204.132,39
$1.200.838,75
$1.197.540,72
$1.194.238,30
$1.190.931,47
$1.187.620,23
$1.184.304,58
$1.180.984,51
$1.177.660,00
$1.174.331,07
$1.170.997,70
$1.167.659,88
$1.164.317,62
$1.160.970,89
$1.157.619,71

$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15
$4.899,15

$1.742,99
$1.738,78
$1.734,57
$1.730,35
$1.726,13
$1.721,90
$1.717,66
$1.713,42
$1.709,17
$1.704,92
$1.700,66
$1.696,39
$1.692,12
$1.687,85
$1.683,56
$1.679,28
$1.674,98
$1.670,69
$1.666,38
$1.662,07
$1.657,75
$1.653,43
$1.649,10
$1.644,77
$1.640,43
$1.636,09
$1.631,74
$1.627,38
$1.623,02
$1.618,65
$1.614,28
$1.609,90
$1.605,51
$1.601,12
$1.596,72
$1.592,32
$1.587,91
$1.583,49
$1.579,07
$1.574,65
$1.570,21
$1.565,77
$1.561,33
$1.556,88
$1.552,42
$1.547,96
$1.543,49

$3.156,15
$3.160,36
$3.164,58
$3.168,80
$3.173,02
$3.177,25
$3.181,49
$3.185,73
$3.189,98
$3.194,23
$3.198,49
$3.202,75
$3.207,02
$3.211,30
$3.215,58
$3.219,87
$3.224,16
$3.228,46
$3.232,77
$3.237,08
$3.241,39
$3.245,71
$3.250,04
$3.254,38
$3.258,71
$3.263,06
$3.267,41
$3.271,77
$3.276,13
$3.280,50
$3.284,87
$3.289,25
$3.293,64
$3.298,03
$3.302,43
$3.306,83
$3.311,24
$3.315,65
$3.320,07
$3.324,50
$3.328,93
$3.333,37
$3.337,82
$3.342,27
$3.346,72
$3.351,19
$3.355,65

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