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 (i) Pay no taxes today, put the money in an interest-yielding account, and pay taxes equal to 25% of the total amount withdrawn at retirement.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.) (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 U.S., 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

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20-03-2021
Business

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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 (i) Pay no taxes today, put the money in an interest-yielding account, and pay taxes equal to 25% of the total amount withdrawn at retirement.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.) (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 U.S., 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

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amcool amcool · Answer 1 · 2021-03-20T19:43:00+01:00

Answer:

a-1. We have:

Expected present discounted value of Plan (i) at 1% interest rate = $1,567.17

Expected present discounted value of Plan (ii) at 1% interest rate after tax = $1,600

a-2. We have:

Expected present discounted value of Plan (i) at 10% interest rate = $1,500

Expected present discounted value of Plan (ii) at 10% interest rate after tax = $1,600

b. Plan (ii) would be chosen in both cases.

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

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(i) Pay no taxes today, put the money in an interest-yielding account, and pay taxes equal to 25% of the total amount withdrawn at retirement.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.)

(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 U.S., 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 choose in each case.

The explanation of the answer is given as follows:

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

a-1. Calculations of expected present discounted value of each of these plans if the interest rate is 1%

Expected future value of plan (i) at 1% after tax = (Amount to save today * (100% + Interest rate)^Number of years) * (100% - Tax rate) = ($2,000 * (100% + 1%)^40) * (100% - 25%) = $2,333.30

Expected present discounted value of Plan (i) at 1% interest rate = Expected future value of plan (i) at 1% after tax / (100%+ interest rate)^Number of years = $2,333.30 / (100% + 1%)^40 = $1,567.17

Expected present discounted value of Plan (ii) at 1% interest rate after tax = Amount to save today * (100% - 20%) = $2,000 * 80% = $1,600

a-2. Calculations of expected present discounted value of each of these plans if the interest rate is 10%

Expected future value of plan (i) at 10% after tax = (Amount to save today * (100% + Interest rate)^Number of years) * (100% - Tax rate) = ($2,000 * (100% + 10%)^40) * (100% - 25%) = $67,888.88

Expected present discounted value of Plan (i) at 10% interest rate = Expected future value of plan (i) at 10% after tax / (100%+ interest rate)^Number of years = $67,888.88 / (100% + 10%)^40 = $1,500

Expected present discounted value of Plan (ii) at 10% interest rate after tax = Amount to save today * (100% - 20%) = $2,000 * 80% = $1,600

b. Which plan would choose in each case.

Plan (ii) would be chosen in both cases because its expected present discounted value of $1,600 is higher in both cases.

Additional Note:

There is no need to calculate the expected present discounted value of Plan (ii) using the interest rates given. This is because it is already in the present period. Only tax is deducted from it.