Mathematics of Finance

Front Cover
H. Holt, 1921 - Business - 280 pages
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Contents

Limitations of simple interest
14
Nominal and effective rates of interest
15
The formulas of compound interest when jm
16
Discount
18
Effective rate with continuous conversion
19
Force of interest
20
Bank discount
21
Force of discount
23
Equated time or average due date
24
Equation of value
27
CHAPTER II
31
Amount of an annuity payable p times a year
35
Present value of an annuity certain
38
Present value of an annuity payable for n years in p instalments per year
41
To find the rate
44
Deferred annuities
47
Annuities due
48
The annuity which I will purchase
52
The annuity which will amount to 1
53
Perpetuities
54
Continuous annuities
56
CHAPTER III
62
Annual payments
63
Amount remaining due after the with payment is made
66
Book value
68
Amount in the sinking fund at any time
69
Retirement of bonded debt when bonds sell at a premium
70
CHAPTER IV
77
The price of a bond to yield a given rate of interest
78
Use of bond tables
84
Amortization of premium at which a bond is bought
85
Accumulation of discount at which a bond is bought
87
Bond purchased between interest payment dates
89
Determination of the investment rate from the purchase price of a given bond
90
ARTICLE PAGE 59 Purchase price of bonds redeemed in instalments
95
Serial bonds
97
Annuity bonds
102
CHAPTER V
107
Constant percentage of book value method
109
Sinking fund method
112
Compound interest method
114
Unit cost method
118
Renewal of th of a plant each year after it reaches full size by
119
equal annual expansion for n years
122
Depreciation of a mining property
125
Capitalized cost of an article
127
Investments to extend service life of an article
128
Composite life of a plant
129
CHAPTER VI
135
Sources of profit
136
Distribution of profits to shareholders
137
Shares issued in series
139
Withdrawal values
140
Time required for stock to mature rate of interest given
141
Compound events
159
Mutually exclusive events
160
Repeated trials
161
Probabilities of life
163
Mortality tables
165
Relations among lx dx px and qx
166
Meanings of npx nqx and nqx
167
Joint life probabilities
169
CHAPTER VIII
172
Life annuity
174
Fundamental relations
175
Annuity due
176
Temporary annuity
177
Commutation columns
179
Other annuities expressed in commutation symbols
180
Annuities with payments m times a year
182
Deferred and temporary annuities payable m times a year
184
Forborne immediate life annuity
186
CHAPTER IX
190
Net single premium
191
Commutation columns C and M
192
Relations of net single premium Ax and present value of life annuity ax
193
Annual premiums
195
Net single premium for term insurance
197
ARTICLE PAGE 118 Annual premium for term insurance
198
Net single premium for endowment insurance
199
Annual premium for endowment insurance
200
CHAPTER X
203
Transformation and verbal interpretation
206
Reserve for limited payment life insurance
207
Reserve for endowment insurance
208
Retrospective method of computing reserves
209
Gross premiums
212
CHAPTER XI
218
Definition of a logarithm
219
Derived properties of logarithms
220
Common logarithms
222
Characteristic
223
Uses of tables
224
To find from the table the logarithm of a given number
225
Computation by means of logarithms
228
Change of base
232
Graph of y log axa 1
234
Exponential and logarithmic equations
235
The series equal to e
238
Exponential series
239
Logarithmic series
240
Calculation of logarithms to base e
241
Logarithms to base 10
242
CHAPTER XII
243
Geometrical progression
245
Number of terms infinite
246
Copyright

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Page 223 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Page 220 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 220 - I. The logarithm of a product equals the sum of the logarithms of the factors.
Page 157 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.
Page 243 - Elements of an arithmetical progression. Let a represent the first term, d the common difference, n the number of terms considered, I the nth, or last, term, and s the sum of the series.
Page 221 - Prop. 4. — The logarithm of any root of a number is the logarithm of the number divided by the number expressing the degree of the root. DEM. — Let a be the base, and x the logarithm of m. Then ar=m. Extracting the £th root we have a"= ^/m.
Page 114 - Engineers appointed to formulate principles and methods for the valuation of railroad property and other public utilities.
Page 266 - ... 3 per cent. ? 4£ per cent. ? 5 per cent. ? 6 per cent. ? 7 per cent. ? 7£ per cent. ? 8 per cent.? 9 per cent. ? 10 per cent.
Page 224 - We shall now proceed to show that the mantissa of the logarithm of a number is independent of the position of the decimal point.
Page 160 - They are said to be mutually exclusive when the occurrence of any one of them on a particular occasion excludes the occurrence of any other on that occasion.

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