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 $3000 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 $3000 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 7.2% annually.
(Please do NOT ROUND when entering “Rates” for any of the questions below)
b2) 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?
How much money will Erich and Mallory have in 45 years if they put away $250
For each part of this question, we take the given parameters & then use these values in the Future Value (FV) function in Excel (or any financial calculator) to find the how much money they will have as follows (Excel formula view showing all calculations is given at the end):
Part a.
Number of periods | Rate of interest | Payment | FV | ||
N PER | I/YR | PMT | |||
a. | 35 | 7.20% | $ -3,000.00 | $ 4,33,237.79 |
Part b.
Number of periods | Rate of interest | Payment | FV | ||
N PER | I/YR | PMT | |||
b. | 10 | 7.20% | $ -3,000.00 | $ 41,842.97 |
b2) If the amount of $41,842.97 (PV) remains invested for next 35 years, we can find its value after 35 years using the following formula with N=35:
Putting the values of PV & N we get
FV= 41,842.97 * (1+7.2%)^35
= $ 4,76,913.95 |
Part C.
Number of periods | Rate of interest | Payment | FV | ||
N PER | I/YR | PMT | |||
c. | 45 | 7.20% | $ -3,000.00 | $ 9,10,151.74 |
Part d.
Here number of periods become 45 x 12 = 540 & monthly interest rate is 7.2%/12= 0.6%
Number of periods | Rate of interest | Payment | FV | ||
N PER | I/YR | PMT | |||
d. | 540 | 0.60% | $ -250.00 | $ 10,11,988.13 |
Part e.
In this case, we are given the required FV which is $1,000,000. So we use Excel's PMT function by entering the given values & finding the PMT
Number of periods | Rate of interest | Payment | FV | ||
N PER | I/YR | PMT | |||
e. | 20 | 7.20% | $ -23,865.21 | $ 10,00,000.00 |
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