Problem 3 a) Alice and Bob have S200,000 in their Investment Retirement Account

Question

Problem 3 a) Alice and Bob have S200,000 in their Investment Retirement Account (IRA) which they need to withdraw over three years. Funds in their IRA earn an annual 10% rate of return and do not get taxed while they are in the IRA. Unfortunately, (for Alice and Bob), withdrawls from their IRA get taxed as income. Alice and Bob would like to maximize the total after tax income over three years. Assume they have an additional fixed income of $30,000 each year from social security. Also assume that their tax rate is 0% for the first $40,000, 10% for the next $40,000, and 25% thereafter e.g. for $90,000 the amount of tax is .1 × 40,000 + .25 × 10,000. Assume that IRA withdrawals are made at the beginning and social security is also received in the beginning. Note that all the money will be withdrawn at the beginning of the third year. Formulate this as an LP. b) Suppose the rate of return in (a) is 0%. Formulate this as a min-cost flow problem (draw the network, and specify the node set, edge set, costs, capacities and demands. No need to write the LP)

Explanation / Answer

(a)

LET THE INCOME FROM IRA IS X AND OTHER INCOME WILL BE Y,

THEN, IF X+Y <=40000;TAX WILL BE NIL,

IF X+Y>40000<80000;TAX WILL BE (80000-40000)*10%=4000;

IF X+Y>80000;THEN TAX WILL BE CHARGED@25%

NOW,TAX FOR FIRST YEAR,

HERE X =10%OF $200000 =$20000

Y =$30000(FIXED)(GIVEN)

THEN ,X+Y = $20000+$30000=$50000

TAX WILL BE ($50000-$40000)*10%=$1000

FOR SECONED YEAR;

X=

X =10%OF $200000 =$20000

Y =$30000(FIXED)(GIVEN)

THEN ,X+Y = $20000+$30000=$50000

TAX WILL BE ($50000-$40000)*10%=$1000

FOR THIRD YEAR;

X=$200000(AS GIVEN IT GET WITHDRAW AT THE BEGINNING OF THIRD YEAR)

Y=$30000

i.e;X+Y=$200000+$30000=$230000

TAX WILL BE FOR FIRST $40000 =NIL

FOR NEXT $40000@10% =10%OF $40000=$4000

FOR REMAINING@25%($230000-$80000)=$150000*25%=37500

TOTAL TAX FOR THIRD YEAR WILL BE =$4000+$37500=$41500

(B)

IF RETURN IS 0%,THEN INCOME FOR FIRST AND SECONED YEAR WILL BE $30000 PER YEAR WHICH IS FIXED.SO,TAX CHARGED WILL BE NIL

AND FOR THE THIRD YEAR ,

INCOME WILL BE $200000+$30000 =$230000

TAX WILL BE FOR FIRST $40000 =NIL

FOR NEXT $40000@10% =10%OF $40000=$4000

FOR REMAINING@25%($230000-$80000)=$150000*25%=37500

TOTAL TAX FOR THIRD YEAR WILL BE =$4000+$37500=$41500

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