V. You want to save $2,000 today for retirement in 40 years. You have to choose
ID: 1170342 • Letter: V
Question
V. 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 i. Pay no taxes today, put the money in an interest-yielding account, and pay taxes equal to 25% of the total amount withdrawn at retirement.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
(a) AT 1%
FIRST CASE : IRA
TAXES ARE PAYABLE AT THE TIME OF WITHDRAWAL AND NOT AT THE TIME OF INVESTMENT
FIRST WE CALCULATE HOW MUCH WILL WILL BE FUTURE VALUE OF SUM AT THE END OF 40 YEARS @1%
FV = 2000 X FVIF @1% FOR 40 YEARS = 2000 X 1.4889 = 2977.8
NOW PAY 25% TAXES AT THE END OF 40 YEARS = 2977.8 -25% TAX = 2333.35
THE PRESENT VALUE @ 1% = 2333.35X PVIF @1% FOR 40 YEARS = 2333.35 X 0.6716 = 1499.92
SECOND CASE : ROTH IRA
HERE WE PAY TAX TODAY AND ON RETIREMENT, NO TAXES ARE PAYABLE
NET INVESTMENT AFTER TAX = 2000 - 20% TAX = 1600
SO PRESENT VALUE OF SUM = 1600 ONLY
(b) AT 10%
FIRST CASE : IRA
FV = 2000 X FVIFA @10% FOR 40 YEARS = 2000 X 45.2593 = 90518.6
NOW PAY 25% TAXES AT THE END OF 40 YEARS = 90518.6 -25% TAX = 67888.95
THE PRESENT VALUE @ 1% = 663888.9 X PVIF @10% FOR 40 YEARS = 67888.95 X 0.0221 = 1500.34
SECOND CASE : ROTH IRA
NET INVESTMENT AFTER TAX = 2000 - 20% TAX = 1600
SO PRESENT VALUE = 1600 ONLY
ANSWER : IN BOTH CASES, ROTH IRA IS BETTER
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