In: Finance
Todd and Jessalyn are 25, 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 $2400 per year to prepare for retirement. Jessalyn just told Todd, though, that she had heard that they would actually have more money the day they retire if they put $2400 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments - than they would have 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 Todd and Jessalyn make an informed decision:
Assume that all payments are made at the end of a year, and that the rate of return on all yearly investments will be 7.2% annually.
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?
Answer a:
Year deposit at the end of year = $2,400
Interest rate = 7.2%
Number of years = 35
To get future value, we will use FV function of excel:
= FV (rate, nper, pmt , pv, type)
= FV (7.2%, 35, -2400, 0, 0)
= $346,590.23
Money will Todd and Jessalyn have in 45 years = $346,590.23
Answer (b):
Time period = 10 years
= FV (7.2%, 10, -2400, 0, 0)
= 33474.37872
= $33,474.38
Money will Todd and Jessalyn have in 10 years = $33,474.38
Answer (b2):
If the money remains invested for the remaining 35 years:
= FV (7.2%, 35, 0, -33474.37872, 0)
= 381531.15985
= $381,531.16
Amount at the of 45 years from now, if it remains invested for the remaining 35 years = $381,531.16
Answer (c):
Time period =45 years, each year amount deposited = $2,400
= FV (7.2%, 45, -2400, 0, 0)
= 728121.3923
= $728,121.39
Money Todd and Jessalyn will have in 45 years = $728,121.39
Answer (d)
Annual rate = 7.2%
Monthly rate (with monthly compounding)= (1 + 7.2%) 1/12 - 1 = 0.58107%
Time period = 45 *12 = 540
= FV (0.58107%, 540, -200, 0, 0)
= $751,860.88
Amount of money Todd and Jessalyn have in 45 years if they put away $200 per month = $751,860.88
Answer (e):
FV = $8,000,000
Time period = 20 years
We will use PMT function to get annual savings/deposit required:
PMT (rate, nper, pv, fv, type)
= PMT (7.2%, 20, 0, -8000000, 0)
= 190921.715451
= $190,921.72
Money they will have to put away at the end of each year for 20 years = $190,921.72