A fortune teller told Madar in 1955 (30 years old) that he is going to die in the year 1995 (when he will be 70 years old). Madar therefore wants to leave behind enough money for his successors after he dies. He has $200,000 savings and he wants to invest in Life Insurance. There are different Life Insurance schemes – Whole Life Insurance and Term Life Insurance. Apart from Life Insurance schemes he can also invest in Stocks. Madar has three different investment options available to him namely Whole life insurance, Term Insurance and Stock investments.

1. IE2110 Operations Research Optimizing your Fortune Ranvir Malhotra U059386W [email_address] Sharad Madar U059385J [email_address] Zhou Wenhan U047762M [email_address]

2. 1955 (30 years old) Year 1995 (70 years old). $200,000 3 Options to Grow his $200,000

3. 50 55 60 65 70 Age Premium Paid over 20 years= $ 38,191 20 Year Payment Option for Whole Life Insurance by NTUC Bought at 30 Years old

4. $100,000 @ Age 70 Least Cost for Term Insurance by NTUC Bought at 30 Years old

5. S&P 500 Stock Returns at Age 70

9. No Choice Available Decision Variable to Vary Year Whole Life Stocks Term Start(i) End(j) Cost Return Wij Cost Return Si Cost Tij 30 35 $540 0 40 $1,200 0 45 $2,220 0 50 $38,191 $58,184 0 $3,120 0 55 $38,191 $67,420 0 $5,100 0 60 $38,191 $79,348 0 $8,160 0 65 $38,191 $94,753 0 $13,260 0 70 $38,191 $114,649 0 $1 4.00 0 $21,840 6 35 40 $660 0 45 $1,680 0 50 $2,940 0 55 $55,817 $85,038 0 $4,560 0 60 $55,817 $98,536 0 $7,620 0 65 $55,817 $115,970 0 $12,720 0 70 $55,817 $138,485 0 $1 8.46 0 $21,660 0 40 45 $1,020 0 50 $2,280 0 55 $4,380 0 60 $85,195 $129,795 0 $6,960 0 65 $85,195 $150,398 0 $12,060 0 70 $85,195 $177,006 0 $1 5.37 0 $21,000 0 Year Whole Life Stocks Term Start(i) End(j) Cost Return Wij Cost Return Si Cost Tij 45 50 $1,440 0 55 $3,360 0 60 $6,840 0 65 $135,137 $205,881 0 $11,040 0 70 $135,137 $238,562 0 $1 5.53 0 $20,160 0 50 55 $2,220 0 60 $5,400 0 65 $14,040 0 70 $229,145 $349,103 0 $1 6.11 0 $18,720 0 55 60 65 70 $1 4.61 0 60 65 70 $1 2.60 0 65 70 $1 1.43 0