Question

suppose that Ramos contributes $5000/year into a traditional IRA earning interest at the rate of 2%/year compounded annually, every year after age 37 until his retirement at age 67. At the same time, his wife Vanessa deposits $3500/year (the amount after paying taxes at the rate of 30%) into a Roth IRA earning interest at the same rate as that of Ramos. Suppose that Ramos withdraws his investment upon retirement at age 67 and that his investment is then taxed at 30%. (Round your answers to the nearest cent.)

(a) How much will Ramos's investment be worth (after taxes) at that time? $

(b) How much will Vanessa's investment be worth at that time? $

Answer 1

Question. Suppose that Ramos contribute $5000/year into a traditional IRA earning interest at the rate of 2℅ year compounded annually, every year after age 37 until his retirement at age 67.

Answer:- (using compound interest formula)

A = P (1 + r/n)^tn

(A = Final account)

(P = Principal or investment)

(r = Interest rate in fraction)

(n = Number of items compound from year)

(t = Time in year)

a) The Ramos's investment be worth (after taxes) at that time will :-

Given that :-

* P = 5000

* r = 2℅

= r = 2/100

=> r = 0.02

* n = 1 (compounded annually)

* t = 67 - 37

=> t = 30

=> Using the formula:-

=> A = P (1 + r/n)^tn

=> A = 5000 (1 + 0.02/1)^30(1)

=> A = 5000 (1.02)^30

* Amount after taxes of 30℅ =

=> 70℅ of A

= 70/100 × 5000(1.02)^30

= 0.7 × 5000 (1.02)^30

= 3500 × 1.81136

= 6339.76

=> Worth of Romos investment after taxes = $ 6339.76

b) The Vanessa's investment be worth at that time will :-

Given that:-

* P = 3500

* r = 2℅

=> r = 0.02

* n = 1

* t = 67 - 37

=> t = 30

Using the formula :-

=> A = P (1 + r/n)nt

=> A = 3500 ( 1 + 0.02/1)^30(1)

=> A = 3500 (1.02)^30

=> A = 3500 × 1.81139

=> A = 6339.76

=> Worth of Vanessa's investment = 6339.76

( Both will have same amount after 30 years)