Question

Use what you have learned about the time value of money to analyze each of the following decisions:

Decision #2: Planning for Retirement

Erich and Mallory 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.   Mallory just told Erich, 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 Erich and Mallory make an informed decision:   

Assume that all payments are made at the END a year (or month), and that the rate of return on all yearly investments will be 7.5% annually.  

(Please do NOT ROUND when entering “Rates” for any of the questions below)

1. How much money will Erich and Mallory 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 Erich and Mallory have in 10 years if they put $1800 per year away for the next 10 years?

3. 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?
4. How much money will Erich and Mallory have in 45 years if they put $1800 per year away for each of the next 45 years?

5. How much money will Erich and Mallory have in 45 years if they put away $150 per MONTH at the end of each month for the next 45 years? (Remember to adjust 7.5% annual rate to a Rate per month!)

6. If Erich and Mallory 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 in order to have $700,000 saved up on the first day of their retirement 45 years from today?

Answer 1

They will have $277652.89 at the end of 45 year if they start investing at the end of 10 year. Calculation is given below:

Similarly, they will have $25464.76 if they start investing $1800 for the next 10 year.

If they do not invest any more dollar then the investment will grow to 25464.76*(1+7.5%)^35=$320063.3

So, if they invest $1800 for the next 45 year they will have (320063.3+277652.89) or $597716.16 at the end of 45 years

Now if the invest $150/month

interest rate=7.5%/12=0.625%, nper=45*12=540

So, they will have 670054.64 at the end of 45 year.

For getting $700000 at the end of 45 year by investing into last 20 year, then -

So, they have put away 16164.3 a year to have fund of $700000 at the end of 45 year.