IV. You want to save $2,000 today for retirement in 40 years. You have to choose
ID: 2406989 • Letter: I
Question
IV. You want to save $2,000 today for retirement in 40 years. You have to choose between the two plans listed in (i) and (ii) i. Pay no taxes today, put the money in an interest-yielding account, and pay taxes equal to 25% of the total amount withdrawn at retirement. (In the U.S., such an account is known as a regular individual retirement account, or IRA Pay taxes equivalent to 20% of the investment amount today, put the remainder in an interest-yielding account, and pay no taxes when you withdraw your funds at retirement. (In the U.S., this is known as a Roth IRA.) ii. What is the expected present discounted value of each of these plans if the interest rate is 196? 10%? Which plan would you choose in each case? a. b.Explanation / Answer
Saving amount = $2,000
Time period = 40 years
If interest rate is 1%
i) $2,000 invested today will become in 40 years = 2,000 x CVF (1%, 40 )
= 2,000 x 1.4889
= $ 2,978
Tax to be paid on maturity = 25% of 2,978
= 2,978 x 25%
= $744
Hence, net value of investment after 40 years (after tax) = 2,978 - 744
= $ 2,234
ii) Tax payable today = 2,000 x 20%
= $400
Hence, net amount available for investment = 2,000 - 400
= $1,600
$1,600 invested today will become in 40 years = 1,600 x CVF (1%, 40 )
= 1,600 x 1.4889
= $ 2,382
b) Since the future value in option (ii) is more than option (i), hence option (ii) should be selected,
If interest rate is 10%
i) $2,000 invested today will become in 40 years = 2,000 x CVF (10%, 40 )
= 2,000 x 45.259
= $ 90,518
Tax to be paid on maturity = 25% of 90,518
= 90,518 x 25%
= $22,629
Hence, net value of investment after 40 years (after tax) = 90,518 - 22,629
= $ 67,889
ii) Tax payable today = 2,000 x 20%
= $400
Hence, net amount available for investment = 2,000 - 400
= $1,600
$1,600 invested today will become in 40 years = 1,600 x CVF (10%, 40 )
= 1,600 x 45.259
= $ 72,414
b) Since the future value in option (ii) is more than option (i), hence option (ii) should be selected,
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