Question

F1360 Unit 3

You are planning to invest in a Roth IRA using a very secure mutual fund that has paid 7% for the past 20 years and is projected to pay at least 7% for the foreseeable future. It is your plan to invest $3000 per year for the next 20 years. At the end of the first 20 years, you will let the Roth IRA fund grow without any more contributions for an additional 20 years. At the end of the 40 year time frame, it is your plan to draw an annuity for 25 years.

1. Solve for the cash value of the Roth IRA at the end of the first 20 years.

2. Solve for the cash value of the Roth IRA at the end of second 20 years.

3. Solve for the cash value of the annual annuity for the remaining 25 years

Answer 1

Part 1:

Cash value at the end of first 20 years= $122,986.48 as follows:

Part 2:

Cash value at the end of second 20 years (F) = P(1+r)^n

Where P= Value after first 20 years ($122,986.48 as above), r= interest rate (given as 7%) and n= period (given as 20 years)

Plugging the values,

Cash value at the end of second 20 years = 122,986.48*(1+7%)^20

=$122,986.48*3.869684462 = $475,918.86

Part 3:

Cash value of annual annuity for the remaining 25 years= $7,524.52 as follows: