Question

Tom and Tricia are 22, newly married, and ready to embark on the journey of life. They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $1800 per year to prepare for retirement.

Tricia just told Tom, though, that she had heard that they would actually have more money the day they retire, if they put $1800 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments - then they would have MORE when they retired than if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do).

Please help Tom and Tricia make an informed decision: Assume that all payments are made at the END of the year, and that the rate of return on all yearly investments will be 8% annually. (Please do NOT ROUND when entering Rates for any of the questions below)

1. How much money will Tom and Tricia have in 45 years, if they do nothing for the next 10 years, then put $1800 per year away for the remaining 35 years?

2. How much money will Tom and Tricia have in 10 years, if they put $1800 per year away for the next 10 years? How much will the amount you just computed grow to if it remains invested for the remaining 35 years, but without any additional yearly deposits being made?

3. How much money will Tom and Tricia have in 45 years if they put $1800 per year away for each of the next 45 years? (This amount can be referred to as their "retirement nest egg")

4. Using your solution to question 3, what is the value in today's dollars, assuming 3% average inflation, of Tom and Tricia's "retirement nest egg"? ("Today", Tom and Tricia are 22 years old. Retirement is 45 years away!)

5. If Tom and Tricia wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end of each year for 20 years assuming an annual interest rate of 8% in order to have $700,000 saved up on the first day of their retirement 45 years from today?

Answer 1

Part 1: Invest $1,800 per year during 35 years:

Amount after 45 years from now= $1,800*FVA(8%,35)= $1,800*172.316804= $310,170.25

Part 2: Deposit $1,800 every year during first 10 years:

Amount after 10 years = $1,800*FVA(8%,10) = $1,800*14.486562= $26,075.81

Amount after 45 years from now, without additional deposits after 10 years=$26,075.81*FVIF(8%,35)

=$26,075.81*14.785344 = $385,539.86

Part 3: Deposit $1,800 each during 45 years:

Amount available after 45 years= $1,800*FVA(8%,45)= $1,800*386.505617 = $695,710.11

Part 4: Value today (retirement nest egg) of part 3 with inflation at 3%

=$695,710.11*PVIF(3%,45)= $695,710.11*0.264439= $183,972.62

Part 5: Start investment after 25 years, to have $700,000 in 20 years (total 45 years from now):

Amount to be deposited every year= $700,000*SFF(8%,20)= $15,296.55 as follows: