You are reading a page from The Mathematical Theory of Investment, Ernest Brown Skinner, (1913)
Part of the American Term Life Insurance History Project
Term Life Insurance

INDEX

Accumulation of discount, 134, 135
Accumulation factor, 67, 70
Accumulation schedule, 184, 135
Actuaries' or Combined Experience
 Mortality Table, 197
American Experience Mortality Table,
 188, 195,197, 209, 241
Amortization, 114, 120; of premium
 on bond,133,134, 136
Amortization equation, 95, 119
Amortization plan, 120
Amortization schedule, 121, 123, 125 ;
 for premium on bond, 134, 135,136,
  137
Amount, 51 ; compound, 54, 55, 56,
  57, 58; table for compound, 220
Amount of annuity, 77, 79, 80, 85, 97,
  110; table for, 228
Annual rent, 77, 93, 95,98,99,115
Annuity, 77 ; amount of, 77, 79, 80,
  85, 97,110 ; certain, 77 ; contingent,
  77; continuous, 92 ; deferred, 77,
  84; deferred life, 192, 197; due, 77,
  84, 85, 204,206 ; forborne,77 ; joint
  life, 192 ; life, 192, 194, 197; rate of
  interest borne by, 109, 110; tempo-
  rary, 192, 197; term of, 77, 97, 99.
  See also Annual rent, Life annuity,
  Present value of annuity
Annuity that 1 will purchase, 95, 96,
  102, 142 ; table for, 236
Annuity that will amount to 1, 93, 94,
 .96, 102, 142
Arithmetical mean, 4
Arithmetical progression, 1, 3, 4
Asset, 150, 151, 152, 156; probable
  life of, 150; wearing value of, 150,
  156
Benefit, 200
Binomial theorem, 106
Book value, 164. See also Bond
Bond, 126; book value of, 133, 134,
  135,187 ; discount on, 127, 132, 134,
  135 ; installment, 140 ; par value of,
  127,131,132,133 ; premium on, 127,
   130, 133, 134, 136; purchase price

  of, 128 ; redemption of, 127 ;  valua-
  tion of,127,138,139
Borrowing shareholder, 170
Building and loan association, 164
Capitalization, 86, 87
Capitalized cost, 89, 90
Certainty, 177
Characteristic, 32
Combinations, 177
Commutation columns, 195, 196; table
   of, 242
Complementary events, 177
Composite age, 157
Composite life, 154, 156
Compound interest. See Interest
Compound interest law, 49, 64
 Computation, of annuities, 101, 195;
   of compound interest, 04 ; by loga-
   rithms, 34 ; of simple interest, 53
 Condition per cent, 159
 Convergence, 16
 Conversion interval, 54, 58
 Death rate, 201, 209, 214
 De Morgan, 196
 Depreciation, 149, 160 ; rate of, 155
 Depreciation fund, 150, 151, 152
 Descartes's rule of signs. 111
 Direct-comparison test, 16
 Discount, 67, 68 ; on bond, 127, 134;
   rate of, 70, 71 ; true, 71, 72
 Discounting factor, 70
 Divergence, 16
 Endowment, 192 ; present value of,
   193
 Endowment insurance. See Insurance
 Engineering News, 140
 Equated time, 74
 Equation,  amortization,  95,  119;
   exponential, 36, 58; sinking-fund,
   142
 Equation of payments, 74; ordinary
   rule for, 75
 Equation of value, 73
Euler's amortization equation, 95,119

243
244  MATHEMATICAL THEORY OF INVESTMENT

Function, 40; algebraic, 41; exponen-
  tial, 49;  logarithmic, 48 ;  rational
  integral, 41; transcendental, 41
Geometrical mean, 4
Geometrical progression, 1, 3, 4
Graph, of exponential function, 49;
  of linear integral function, 45; of
  logarithmic function, 48; of quad-
  ratic integral function, 47
Graphical representation, 41
Gruhl, Edwin, 159
Hagenah, W. J., 154
Hatfield, H. R., 144
Hickerson, 91
Hoskold, H., 162
Impossibility, 177
Infinite  series,  10;  with  constant
  terms, 14
Installment bonds, 140
Insurance, 200, 214 ; endowment, 207,
  208; term, 201, 205, 206 ; whole life,
  201, 202-
Interest, 51; compound, 54, 55, 59, 61,
  64 ; computation of compound, 64 ;
  computation of simple, 53; exact,
  52; force of, 61 ; instantaneous com-
  pound, 61 ; ordinary, 52 ; simple,
  51; table for exact, 219. See also
  Rate of interest
Interest-bearing debts, 114
Interstate Commerce Commission, 154
Legal-reserve life insurance, 200
Life annuity, 192, 194, 195, 197, 198,
  203 ; computation of, 195 ; deferred,
  192,197 ; due, 192 ; present value of,
  194, 197, 198; temporary, 192, 197,
  198
Limit, 7, 10, 12
Limited payment life policy, 203
Loading, 212, 213
Loan value, 211
Logarithm, 29, 30; Briggsian, 30;
 hyperbolic, 30 ; Napierian, 30
Logarithms, computation by, 34 ; sys-

Mantissa, 32
Mathematical expectation, 186, 193,
 205
Matheson, 160
Mean, arithmetical, 4 ; geometrical, 4
Mining properties, valuation of, 160
Modulus, 38

Mortality table, 186, 187, 188, 197,
  201, 202, 214; Actuaries' or Com-
   bined Experience, 197; American
  Experience,188,195,197, 209, 241
Mutual Life Insurance Company, 188,
   191
Net annual premium, 203 ; for endow-
  ment insurance, 208; for n-payment
  life policy, 204 ;  for ordinary life
  policy, 203 ; for term insurance, 206
Net premium, 201
Net single premium, 201; for en-
  dowment insurance, 207 ; for term
  insurance, 205; for wliole life in-
  surance, 202
Net value of policy, 209
Nominal par value, 127
Nominee, 192
Number of day of year, 53 ; table for,
  218
Old-line life insurance, 200
Ordinary life policy, 203; terminal
  reserve for, 210
Origin of coordinates, 40
Par value of bond, 127, 128, 131, 133,
  134, 136
Permutations, 177
Perpetuity, 77, 86, 87
Policy of insurance, 200 ; limited pay-
  ment, 203, 204 ; ordinary life, 203;
  valuation of, 209
Policy year, 200
Policyholder, 200
Premium, gross, 200, 212, 213; level,
  209; net, 201; office, 200, 213. See ,
  also Net annual premium and Net
  single premium
Premium on bond, 127,130 ; amortiza-
  tion of, 133, 136; computation of,
  130
Present value, 68 ; of continuous an-
 nuity, 93 ; of deferred annuity, 85 ;
 of deferred life annuity, 197 ; of en-
 dowment 193; of life annuity, 192,
  194; of perpetuity, 86, 87, 89; of
 temporary annuity, 198; table for,
 224. See also Present value of annuity
Present value of annuity, 78, 82, 84,
 95, 99, 115, 124, 141, 161 ; table for,
 232
Present worth, 68
Probability, 175 ; compound, 180,183;
 partial, 179,189; relative, 179; total,
 179, 183, 189
INDEX

245

Probable life, 150, 162, 163, 154, 156
Profit, rate of, 165
Profits, net, 164
Progression, arithmetical, 1, 3, 4; geo-
 metrical, 1, 3, 4, 79, 80, 82, 83; in-
 finite geometrical, 6, 88
Kate, of depreciation, 155; of dis-
 count, 70
Rate of interest, 51, 109, 171; borne
 by annuity, 109 ; effective, 59, 60,
 61. 63, 69, 167; nominal, 59, 60, 61,
 62. 79, 80, 82, 83; paid by borrow-
 ing shareholder, 170 ; practicable,
 162;  realized by investor,  167;
 stipulated, 162
Redemption fund, 161
Reserve, terminal, 209, 210
Residual value, 150
Schedule for accumulation of discount,
 134,135
Schedule for amortization, 122, 123,
 124,125, 126 ; of premium on bond,
 134,136, 137
Schlimbach, 126
Scrap value, 150
Sequence, 10, 11,12
Series, 10, 11, 16; binomial, 24; ex-
 ponential, 26; logarithmic, 28, 62,
 63; power, 23; with constant terms,
 14

Sinking fund, 142, 143, 144, 150
Sinking-fund problem, 94
Slope of straight line, 47
Surplus, 214
Surrender charge, 212
Temporary annuity, 197, 204, 208;
 present value of, 198
Term of an annuity, 97
Term insurance, 201, 205; premium
 for, 206
Terminal reserve, 209; for ordinary
 life policy, 210
Test-ratio test, 16, 19
Valuation, of bonds, 127; of mining
 properties, 160 ; of policy, 209, 210
Value, cash surrender, 211 ; depreci-
 able, 150 ;  equation of, 73 ;  loan,
 211 ; of mine, 161; residual, 150;
 scrap, 150 ; wearing, 150, 156, 157;
 withdrawal, 164
Van Hise, 67
Variable, 10; dependent and inde-
 pendent, 41
Wearing value, 150, 156, 157 ; curve
 of, 157
Whole life insurance, 201, 202
Wisconsin Railroad Commission, 159
Zero point, 40