3. Life Annuities and Life Insurance (10 marks) (a) At age 35, David buys a 6-year temporary life annuity of $10,000 per annum to be paid at the beginning of each year for his retire- ment. Find a net single premium for David, if the first payment is made at age 65. Assume that r(t) = 5%. (5 marks) (b) A man currently aged 45 purchases a 5-year term insurance that pays a benefit of $90,000 with r = 4%. Find the net single pre- mium of the death benefit. (5 marks) 10655 9848 2 3 4 905600 9947545 9937697 9927958 9739 1.07 0.99 0.98 0.95 1 52 53 54 5906492 841435 8771057 8694661 6017 70378 76396 8121 TW 7.9% 8.71 9.56 9432 5 6 7 g 9 91526 9909599 9901077 9893156 9885637 8027 8522 7921 7519 7325 0.90 0.86 0.80 0.76 0.74 55 56 57 58 59 8611540 8521377 8423722 318510 8205461 9013 97655 105212 113049 121195 10.47 11.46 12.49 13.59 14.77 10 11 12 13 14 9878322 871111 9863510 9655126 9845369 7211 701 6384 9757 11322 0.73 0.77 0.85 0.99 1.15 0 61 62 63 4 808426 7954271 7814753 76478 7503368 129995 139518 149965 161420 173628 16.08 17.54 19.19 21.06 23.14 15 16 17 18 19 9834047 920968 9806138 9789762 772336 13079 14830 16376 17426 18177 1.33 1.51 1.67 1.76 1.86 65 66 6 9 7329740 7143418 6944474 6733084 6509613 186322 198944 211390 223471 235453 25.42 27.85 30.44 33.19 36.17 0 21 22 3 24 9754159 9735626 9717031 9698666 9680626 18533 18595 18365 18040 17619 1.90 1.91 1.80 1.86 1.82 70 71 72 73 74 6274160 026268 5765331 5490613 5201587 247892 260937 274718 289026 302680 39.51 43.30 47.65 52.64 58.19 25 26 7 28 29 9663007 9645903 9629216 9612750 9596408 17100 16687 16466 16342 16410 1.77 1.73 1.71 1.70 1.71 75 76 TT 78 79 4898907 4584446 4261105 3932489 3602553 314461 323341 328616 329936 328012 64.19 70.53 77.12 83.90 91.05 16573 17023 30 31 32 34 9579998 9563425 546402 528932 9510732 17470 18200 19021 1.73 1.78 1.83 1.91 2.00 80 81 82 83 4 3274541 2950885 2633724 2324920 2026726 323656 317161 308804 29819 284248 98.84 107.48 117.25 128.26 140.25 35 38 37 8 39 9491711 9471683 9450466 9427785 9403461 20028 21217 2261 24324 2.11 2-24 2.40 2.58 2.79 85 86 8 9 1742478 1475966 1230823 1009829 814659 266512 245143 220994 195170 168871 152.95 166.09 179.55 193.27 207,29 26236 0 41 42 9377225 9348906 9318148 9284975 9249042 28319 30758 3173 35933 38753 3.02 3.29 3.56 3.7 4.19 0 91 92 93 4 645788 502572 383472 286281 208381 143216 119100 97191 TT900 61660 221.77 2366.98 253.45 272.11 295.00 4 5 46 7 48 9 921028 9168382 9123274 9074738 022649 41907 45108 48536 52089 56031 4.55 4.92 5.32 5.74 6.21 95 5 97 8 9 146721 96309 60504 31450 10757 48412 37805 20054 20693 10757 329.6 384.55 460.20 57.98 1000.00