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Pay no taxes today, put the money in an interest-yielding account, and pay taxes equal to \(20 \%\) of the total amount withdrawn at retirement. (In the United States, such an account is known as a regular individual retirement account [IRA].)

ii. Pay taxes equivalent to \(30 \%\) 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 United States, this is known as a Roth IRA.)

a. What is the expected present discounted value of each of these plans if the real interest rate is \(1 \%\) ? \(10 \%\) ?

b. Which plan would you choose in each case?