Question

James and Shannon 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. Shannon just told James, 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).

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.

a) How much money will James and Shannon have in 45 years if they do nothing for the next 10 years, then puts $2400 per year away for the remaining 35 years?

b) How much money will James and Shannon have in 10 years if they put $2400 per year away for the next 10 years?

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?

c) How much money will James and Shannon have in 45 years if they put $2400 per year away for each of the next 45 years?

d) How much money will James and Shannon have in 45 years if they put away $200 per MONTH at the end of each month for the next 45 years? (Remember to adjust the 9% annual rate to a Rate per month!) (Round this rate per month to 5 places past the decimal) example of rounding: .062134 = .06213 or 6.213%

e) If James and Shannon 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 $8,000,000 saved up on the first day of their retirement 45 years from today?

Answer 1

FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Solution A
Amount after 45 years	= 2400* ((((1 + 7.2%) ^ 35) - 1) / 7.2%)
Amount after 45 years	346,590.23
Solution B
Amount after 10 years	= 2400* ((((1 + 7.2%) ^ 10) - 1) / 7.2%)
Amount after 10 years	33,474.38
Solution B2
Amount after 35 years	=33474.38*(1+7.2%)^35
Amount after 35 years	381,531.17
Solution c
Amount after 45 years	= 2400* ((((1 + 7.2%) ^ 45) - 1) / 7.2%)
Amount after 45 years	728,121.39
Solution D
Effective rate for monthly contribution	(1+7.2%/12)^12)-1)
Effective rate for monthly contribution	7.442%
Amount after 45 years	= 2400* ((((1 + 7.7.442%) ^ 45) - 1) / 7.2%)
Amount after 45 years	809,590.50
Solution D
8000000	= Per year investment* ((((1 + 7.2%) ^ 20) - 1) / 7.2%)
8000000	= Per year investment* 41.911
Per year investment=	8000000/41.911
Per year investment=	190,880.68