Regular IRAs versus Roth IRAs 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Pay no taxes today, put the money in an interest-yielding account, and pay taxes equal to \(25 \%\) of the total amount withdrawn at retirement.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 United States, such an account is known as a regular individual retirement account [IRA].)

ii. 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 United States, this is known as a Roth IRA.)

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

b. Which plan would you choose in each case?