Question

Dan and Wayne are brothers who intend to begin saving money for retirement when each is exactly age 25. Each brother intends to save $4,800 per year before taxes and invest the money to accumulate wealth and to provide income in retirement. Dan plans to invest his savings into a Traditional IRA and anticipates an average annual return of 10%. Wayne plans to invest his savings into a Roth IRA and also anticipates an average annual return of 10%. Both brothers expect to have an annual income tax rate of 25% during their working years and also in their retirement years. 1) How much money will Dan have in his Traditional IRA Investment Account at age 67 If a 25 year annuity is purchased with this sum of money at age 67, how much annual income after taxes will be provided if the annuity contract has a 4% interest rate? 2) How much money will Wayne have in his Roth IRA Investment Account at age 67 $ If a 25year annuity is purchased with this sum of money at age 67, how much annual income after taxes will be provided if the annuity contract has a 4% interest rate? $ What conclusions can you determine from this analysis? Briefly Explain.

Answer 1

(1) Dan will have $ 35,341 (approx) in his traditional IRA account at age 67

the above sum is calculated by assuming that interest earned is re-invested and thus present value annuity factor @ 10% for 42years (67-25) is 9.817 (approx)

If 25 years annuity is purchased with the above sum i.e. $ 35,341 then annual income after taxes at 4% interest rate will be $1696.69 9approx) which is calculated as = [$35,341 (1-0.25)] / 15.622 (Present value annuity factor @ 4%)

(2) Wayne will have $ 35,341 (approx) in his traditional IRA account at age 67

the above sum is calculated by assuming that interest earned is re-invested and thus present value annuity factor @ 10% for 42years (67-25) is 9.817 (approx)

If 25 years annuity is purchased with the above sum i.e. $ 35,341 then annual income after taxes at 4% interest rate will be $1696.69 9approx) which is calculated as = [$35,341 (1-0.25)] / 15.622 (Present value annuity factor @ 4%)