FM for Actuaries

Recommendations

Info

Answers to Selected Exercises 3436.17 $7.4785 discount6.18 3.6%6.19 (a) At maturity (b) At the end of the 6th year6.20 P (1 + i) t − t(Fr)6.21 Book value B 3 = $102.0129, other results follow6.22 $1.2578 write-up6.24 $1,0456.26 $102.12206.27 $36.676.28 $3.83 discount6.29 (a) $99.9399 (b) $104.29416.30 (a) At issue: $107.1062, after 7 months: $94.3933 (b) 16.3%6.32 $1,610.50Chapter 77.1 (a) 8.52% convertible semiannually (b) 7.41% convertible semiannually(c) $1,036.517.2 $1,053.89, 8.30% convertible semiannually7.3 11.12% convertible semiannually7.4 (a) 7.40% convertible semiannually (b) $1,0677.5 (a) 9.746% (b) 9.833% (c) 9.654%; all compounded semiannually7.6 3.962%7.7 (a) exp(0.03t) for t ≤ 5 and exp[0.06 + 0.0025(1 + t) 2 ] for t>5(b) $135.9413 (c) 3.142% compounded semiannually7.8 4.44%7.11 7.3678%
344 APPENDIX B7.12 (a) 3.0205% (b) 1007.13 (a) 5.0% convertible semiannually (b) 4.0%(c) 8.23% convertible annually7.14 (a) 3.78% (b) 4.01%7.15 (a) 7.073% (b) 6.801%7.16i H for Bond A over 3 years are 5.3222% (Scenario Up)and 5.8077% (Down),i H for Bond B over 3 years are 5.1974% (Scenario Up)and 5.1769% (Down).7.17 4.0816%, 5.1957%, 6.8937%, 7.7320%7.18 2.0408%, 2.5978%, 5.6145%, 7.1794%7.21 3.0393%7.22 4.0816%, 5.5723%, 5.0000%, 5.9589%, 6.3708%, 6.7790%7.23 8.0811%, 8.2078%, 8.3582%, 8.6505%Chapter 88.1 D ∗ =4.2772, C =24.40708.2 D =3.9346, C =20.54588.5 21 years8.9 Statement A8.10 Statement B8.11 4.752 years8.14 (a) +2.768% (b) +2.828%8.16 260.95668.17 (a) P = 350.409, D ∗ =5.4045 years, C =48.0435(b) Approximate value = 341.151, true value = 341.147
Page 2 and 3:
Financial Mathematics forActuaries
Page 4 and 5:
Financial Mathematics forActuaries
Page 6 and 7:
To Bonnie, Nikki and Kevinfor their
Page 8 and 9:
About the AuthorsWai-Sum Chan, PhD,
Page 10 and 11:
Preface to the Second EditionA good
Page 12 and 13:
ContentsAbout the AuthorsPreface to
Page 14 and 15:
ContentsxiiiChapter 7 Bond Yields a
Page 16 and 17:
List of Mathematical SymbolsSymbola
Page 18 and 19:
List of Mathematical SymbolsxviiSym
Page 20 and 21:
1InterestAccumulation andTime Value
Page 22 and 23:
Interest Accumulation and Time Valu
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48:
Table 1.3:Summary of accumulated va
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
2AnnuitiesAn annuity is a series of
Page 61 and 62:
Annuities 41Figure 2.1 illustrates
Page 63 and 64:
Annuities 43Solution: The rate of i
Page 65 and 66:
Annuities 45As an annuity-due of n
Page 67 and 68:
Annuities 47Figure 2.3: Illustratio
Page 69 and 70:
Annuities 49Also, it can be checked
Page 71 and 72:
Annuities 512.5 Payment Periods, Co
Page 73 and 74:
Annuities 53Note that (2.20) has a
Page 75 and 76:
Annuities 55Example 2.11: Solve the
Page 77 and 78:
Annuities 57Figure 2.8:Increasing a
Page 79 and 80:
Annuities 59Second, we may consider
Page 81 and 82:
Annuities 61n is an integer and 0 <
Page 83 and 84:
Annuities 63Exhibit 2.1: Use of Exc
Page 85 and 86:
Annuities 652.2 Let d (2) =2%. Eval
Page 87 and 88:
Annuities 672.23 Express s(52) n⌉
Page 89 and 90:
Annuities 692.37 A paused rainbow i
Page 91 and 92:
Annuities 71(c) Find the amount of
Page 93 and 94:
3SpotRates, Forward Ratesand the Te
Page 95 and 96:
Spot Rates, Forward Rates and the T
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
4Rates of ReturnThe performance of
Page 127 and 128:
Rates of Return 107Example 4.1: A p
Page 129 and 130:
Rates of Return 109where y 4 is the
Page 131 and 132:
Rates of Return 111Exhibit 4.3:Solu
Page 133 and 134:
Rates of Return 113Figure 4.1: Cash
Page 135 and 136:
Rates of Return 115Hence, from (4.5
Page 137 and 138:
Rates of Return 117Calculate the ar
Page 139 and 140:
Rates of Return 119denote it as R D
Page 141 and 142:
Rates of Return 1214.4 Portfolio Re
Page 143 and 144:
Rates of Return 123Solution: For (a
Page 145 and 146:
Rates of Return 125To calculate the
Page 147 and 148:
Rates of Return 127Finally, for (d)
Page 149 and 150:
Rates of Return 129Figure 4.4: NPV
Page 151 and 152:
Rates of Return 131When the project
Page 153 and 154:
Rates of Return 133measure of the r
Page 155 and 156:
Rates of Return 1354.7 Which of the
Page 157 and 158:
Rates of Return 1374.19 A 7-year pr
Page 159 and 160:
Rates of Return 139(a) Calculate th
Page 161 and 162:
Rates of Return 141Assume all inves
Page 163 and 164:
Rates of Return 143(a) Draw a graph
Page 165 and 166:
Rates of Return 1454.50 Judy is con
Page 167 and 168:
5Loans andCosts of BorrowingLoans a
Page 169 and 170:
Loans and Costs of Borrowing 149can
Page 171 and 172:
Loans and Costs of Borrowing 151Due
Page 173 and 174:
Loans and Costs of Borrowing 153Tab
Page 175 and 176:
Loans and Costs of Borrowing 155Exa
Page 177 and 178:
Loans and Costs of Borrowing 157We
Page 179 and 180:
Loans and Costs of Borrowing 159Exa
Page 181 and 182:
Loans and Costs of Borrowing 161For
Page 183 and 184:
Loans and Costs of Borrowing 1635.5
Page 185 and 186:
Loans and Costs of Borrowing 165the
Page 187 and 188:
Loans and Costs of Borrowing 167its
Page 189 and 190:
Loans and Costs of Borrowing 169Not
Page 191:
Table 5.5:Summary of reference rate
Page 194 and 195:
Page 196 and 197:
Loans and Costs of Borrowing 175rem
Page 198 and 199:
Loans and Costs of Borrowing 177Yea
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
Loans and Costs of Borrowing 185let
Page 208 and 209:
6Bondsand Bond PricingA bond is a c
Page 210 and 211:
Bonds and Bond Pricing 189hand, bon
Page 212 and 213:
Bonds and Bond Pricing 191Figure 6.
Page 214 and 215:
Bonds and Bond Pricing 193Example 6
Page 216 and 217:
Bonds and Bond Pricing 195Table 6.1
Page 218 and 219:
Bonds and Bond Pricing 197Note that
Page 220 and 221:
Bonds and Bond Pricing 199Figure 6.
Page 222 and 223:
Bonds and Bond Pricing 201The Excel
Page 224 and 225:
Bonds and Bond Pricing 203Assuming
Page 226 and 227:
Bonds and Bond Pricing 205cash flow
Page 228 and 229:
Bonds and Bond Pricing 2076. When t
Page 230 and 231:
Bonds and Bond Pricing 209Half- Cou
Page 232 and 233:
Bonds and Bond Pricing 2116.23 Show
Page 234 and 235:
7Bond Yields andthe Term StructureW
Page 236 and 237:
Bond Yields and the Term Structure
Page 238 and 239:
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
8Bond ManagementThe rate of interes
Page 268 and 269:
Bond Management 247Using PV(C t ) a
Page 270 and 271:
Bond Management 249again is less th
Page 272 and 273:
Bond Management 251To use the modif
Page 274 and 275:
Bond Management 253Example 8.5: A 1
Page 276 and 277:
Bond Management 255Figure 8.2:Bond-
Page 278 and 279:
Bond Management 257Rule 3: Other th
Page 280 and 281:
Bond Management 259the duration D P
Page 282 and 283:
Bond Management 261Example 8.8: A c
Page 284 and 285:
Bond Management 263Figure 8.4:Illus
Page 286 and 287:
Bond Management 265Example 8.10: A
Page 288 and 289:
Bond Management 267of the asset and
Page 290 and 291:
Bond Management 269Figure 8.5:Illus
Page 292 and 293:
Bond Management 271Solving the abov
Page 294 and 295:
Bond Management 273First, in classi
Page 296 and 297:
Bond Management 275wherePV(C t )=C
Page 298 and 299:
Bond Management 277Example 8.14: Co
Page 300 and 301:
Bond Management 2795. Immunization
Page 302 and 303:
Bond Management 281Time toCoupon ra
Page 304 and 305:
Bond Management 2838.15 Using Exerc
Page 306 and 307:
Bond Management 2858.22 Revisit Exe
Page 308 and 309:
Bond Management 2878.29 Suppose you
Page 310 and 311:
Bond Management 289(c) Calculate th
Page 312 and 313:
9Interest Rates andFinancial Securi
Page 314 and 315: Interest Rates and Financial Securi
Page 326 and 327: 10Stochastic Interest RatesIn previ
Page 328 and 329: Stochastic Interest Rates 307Table
Page 330 and 331: Stochastic Interest Rates 309ands 5
Page 332 and 333: Stochastic Interest Rates 311Next,
Page 334 and 335: Stochastic Interest Rates 313Theref
Page 336 and 337: Stochastic Interest Rates 315which
Page 338 and 339: Stochastic Interest Rates 317There
Page 340 and 341: Stochastic Interest Rates 319We use
Page 342 and 343: Stochastic Interest Rates 32110.3 W
Page 344 and 345: Stochastic Interest Rates 32310.13
Page 346 and 347: Stochastic Interest Rates 32510.24
Page 348 and 349: APPENDIXAReview of Mathematics and
Page 350 and 351: Review of Mathematics and Statistic
Page 352 and 353: Review of Mathematics and Statistic
Page 354 and 355: APPENDIXBAnswers to Selected Exerci
Page 356 and 357: Answers to Selected Exercises 335Ch
Page 358 and 359: Answers to Selected Exercises 337Ch
Page 360 and 361: Answers to Selected Exercises 3394.
Page 368 and 369: Answers to Selected Exercises 34710
Page 370 and 371: IndexAaccrued interest, 187, 198-20
Page 372 and 373: Index 351RATE, 63, 70XIRR, 109-111,
Page 374: Index 353dollar-weighted, 105, 112,
show all

FM for Actuaries

Create successful ePaper yourself

Delete template?

Save as template?