Suppose that Ramos contributes $4000/year into a traditional IRA earning interest at the rate of 5%/year compounded annually, every year after age 35 until his retirement at age 65.

Question

Suppose that Ramos contributes $4000/year into a traditional IRA earning interest at the rate of 5%/year compounded annually, every year after age 35 until his retirement at age 65. At the same time, his wife Vanessa deposits $2700/year into a Roth IRA earning interest at the same rate as that of Ramos and also for a period of 30 years. Suppose that the investments of both Ramos and Vanessa are in a marginal tax bracket of 35% at the time of their retirement and that they both wish to withdraw all of the money in their IRAs at that time.

(a) After all due taxes are paid, who will have the larger amount?

(b) How much larger will that amount be? (Round your answer to the nearest cent.)

Answer 1

Both A and B can be calculated at the same time, first we need to find the FV of both of their IRAs, this can be done using the future value of an annuity formula:

FV=PMT*((1+i)ⁿ-1)/i Future Value = Payments * ((1+interest rate)^{number of periods}-1)/interest rate

Ramos FV=4000(1.05³⁰-1)/.05=265755.39

Now we have to take out takes because this was a traditional IRA:

265755.39*65%=$172,741

Vanessa FV=2700(1.05³⁰-1)/.05=$179,384.89 (since Vanessa used a ROTH and paid taxes before putting money in her IRA she does not get taxed where she withdraws her money

a) Vanessa will have more money

b) Vanessa will have $6643.89 more than Ramos