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Optimizing your Fortune

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Information about Optimizing your Fortune
Finance

Published on November 20, 2008

Author: ybother

Source: slideshare.net

Description

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

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

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

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

S&P 500 Stock Returns at Age 70

30 year old guy, non-smoker who will die at the age of 70 Profile of Person to base our insurance cost upon Income = Expense So that he only has 1 lump sum to invest at the start Whole Life can only be surrendered after 20 years Because we do not have the surrender and death value under 20 years He can’t buy any insurance after he is 50 years old Because Whole life must be bought for 20 years or more He can change his portfolio after every 5 years To reduce number of decision variables Whole Life non-guaranteed is 5.25% per annum Following Projections

30 year old guy, non-smoker who will die at the age of 70

Profile of Person to base our insurance cost upon

Income = Expense

So that he only has 1 lump sum to invest at the start

Whole Life can only be surrendered after 20 years

Because we do not have the surrender and death value under 20 years

He can’t buy any insurance after he is 50 years old

Because Whole life must be bought for 20 years or more

He can change his portfolio after every 5 years

To reduce number of decision variables

Whole Life non-guaranteed is 5.25% per annum

Following Projections

Decision Variable At every 5 year, how much of stocks, whole life and term insurance should he buy? W ij  units of $100,000 Whole Life policies taken at year i and surrender at year j T ij  units of $100,000 Term policies taken at year i until year j S i  Dollar amount invested in stocks purchased at year I Objective Function Maximize money at death = age J 70 Maximize Z = Σ (R wij * W ij ) + Σ (R si * S i ) + (Σ T ij (j = 70) * 100,000); Constraints $200,000 of spending maximum Σ (Cost wij * W ij ) + Σ (Cost tij * T ij ) + Σ S i = 200,000 Required at least $400,000 insurance at any time At age i: W ij + T ij ≥=4

At every 5 year, how much of stocks, whole life and term insurance should he buy?

$200,000 of spending maximum

Required at least $400,000 insurance at any time

Return Coefficients for Objective Function Stock Historical 5 Year Growth Whole Life Guaranteed: $100,000 Non- Guaranteed: Growth = 5.25% Per Annum Cost Coefficients for Constraints Stock -Cost=1 Whole Life Fixed Monthly Cost for 20 years Term Least Cost Solution for each starting and ending Year

Return Coefficients for Objective Function

Stock

Historical 5 Year Growth

Whole Life

Guaranteed: $100,000

Non- Guaranteed: Growth

= 5.25% Per Annum

Cost Coefficients for Constraints

Stock

-Cost=1

Whole Life

Fixed Monthly Cost for 20 years

Term

Least Cost Solution for each starting

and ending Year

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    

At age 30, buy $112,640 in Stocks and $87,360 in Term Insurance Return of $1,846,297 when he dies at the age of 70. Only buy stocks at age 30 Either buy Whole Life only Term + Stocks Whole Life + Stocks Stock Returns Take stock + term when stock % > 8% Take whole life when stock % < 7% Take either when stock return is between 7%and 8%

At age 30, buy $112,640 in Stocks and $87,360 in Term Insurance

Return of $1,846,297 when he dies at the age of 70.

Only buy stocks at age 30

Either buy

Whole Life only

Term + Stocks

Whole Life + Stocks

Take whole life when

stock % < 7%

Flexibility buy and sell stock every 5 years Non constant growth in whole life returns

Flexibility buy and sell stock every 5 years

Non constant growth in whole life returns

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