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Use the table to calculate the minimum premium an insurance company should charge for a $5 million three-year term life insurance contract issued to a man aged 60. Assume that the premium is paid at the beginning of each year and death occurs halfway through a year. The risk-free interest rate is 6% per annum (with semiannual compounding).

Probability Expectat Table 3.1 Male Female Survival Probability of Death within 1 Year Probability of Death within 1 Year Age (Years) Life Expectancy Survival Probability Ville 0 1 0.006519 0.000462 0.000291 0.000209 1.00000 0.99348 0.99302 0.99273 76.28 75.78 74.82 73.84 0.005377 0.000379 0.000221 0.000162 1.00000 0.99462 0.99425 0.99403 2 3 7952 78.54 ... 30 31 32 33 0.001467 0.001505 0.001541 0.001573 0.97519 0.97376 0.97230 0.97080 47.82 46.89 45.96 45.03 0.000664 0.000705 0.000748 0.000794 0.98635 0.98569 0.98500 0.98426 51.04 50.98 49.11 ..4 40 41 42 43 0.002092 0.002240 0.002418 0.002629 0.95908 0.95708 0.95493 0.95262 38.53 37.61 36.70 35.78 0.001287 0.001393 0.001517 0.001662 0.97753 0.97627 0.97491 0.97343 42.43 41.48 40.54 39.60 ... ... 50 51 52 53 0.005038 0.005520 0.006036 0.006587 0.92940 0.92472 0.91961 0.91406 29.58 28.73 27.89 27.05 0.003182 0.003473 0.003767 0.004058 0.95829 0.95524 0.95193 0.94834 33.16 32.27 31.38 30.49 60 61 62 63 0.011197 0.012009 0.012867 0.013772 0.86112 0.85147 0.84125 0.83042 21.48 20.72 19.97 19.22 0.006545 0.007034 0.007607 0.008281 0.91526 0.90927 0.90287 0.89600 24.46 23.62 22.78 21.95 70 71 72 0.023528 0.025693 0.73461 0.71732 14.24 0.015729 12 Probability Expectat Table 3.1 Male Female Survival Probability of Death within 1 Year Probability of Death within 1 Year Age (Years) Life Expectancy Survival Probability Ville 0 1 0.006519 0.000462 0.000291 0.000209 1.00000 0.99348 0.99302 0.99273 76.28 75.78 74.82 73.84 0.005377 0.000379 0.000221 0.000162 1.00000 0.99462 0.99425 0.99403 2 3 7952 78.54 ... 30 31 32 33 0.001467 0.001505 0.001541 0.001573 0.97519 0.97376 0.97230 0.97080 47.82 46.89 45.96 45.03 0.000664 0.000705 0.000748 0.000794 0.98635 0.98569 0.98500 0.98426 51.04 50.98 49.11 ..4 40 41 42 43 0.002092 0.002240 0.002418 0.002629 0.95908 0.95708 0.95493 0.95262 38.53 37.61 36.70 35.78 0.001287 0.001393 0.001517 0.001662 0.97753 0.97627 0.97491 0.97343 42.43 41.48 40.54 39.60 ... ... 50 51 52 53 0.005038 0.005520 0.006036 0.006587 0.92940 0.92472 0.91961 0.91406 29.58 28.73 27.89 27.05 0.003182 0.003473 0.003767 0.004058 0.95829 0.95524 0.95193 0.94834 33.16 32.27 31.38 30.49 60 61 62 63 0.011197 0.012009 0.012867 0.013772 0.86112 0.85147 0.84125 0.83042 21.48 20.72 19.97 19.22 0.006545 0.007034 0.007607 0.008281 0.91526 0.90927 0.90287 0.89600 24.46 23.62 22.78 21.95 70 71 72 0.023528 0.025693 0.73461 0.71732 14.24 0.015729 12