Question

Decision #2: Planning for Retirement

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 8.4% annually.

A. How much money will Todd and Jessalyn 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 Todd and Jessalyn have in 10 years if they put $2400 per year away for the next 10 years?

B-2) 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 Todd and Jessalyn have in 45 years if they put $2400 per year away for each of the next 45 years?

D. How much money will Todd and Jessalyn 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 8.4% 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 Todd and Jessalyn 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 $1,000,000 saved up on the first day of their retirement 45 years from today?

Answer 1

Answer:

A)

Number of years: 45

Payment to start in 10 years

Annual payment (at the end of the year: $2400

Number of payments: 35; of which number of payments that will earn interest, 34, since all payments are to be made at the end of the year

Value in 35 years: 2,400+2400FVIFA_8.4%,34

2400*[(1.084^34)-1]/.084 = $414,963 + $2,400 = $417,363

Amount available in 35 years: $417,363

B)

Annual payment: $2,400

Period: 10 years

Amount available in 10 years: $2,400+2400FVIFA_8.4%,9 = $32,875

Therefore, the amount available in 10 years: $32,875

If this is invested for the next 35 years, the amount available at the end of the 35^th year:

$32,875*(1.0840^35) = $553,211

Therefore the amount available at the end of the 35^th year = $553,211

C)

Number of years: 45

Payment made at the end of each year: $2,400

Value at the end of 45^th year: 2,400+2400FVIFA_8.4%,45 = $1,050,931

Therefore, the amount available at the end of the 35^th year = $1,050,931

D)

Monthly payment: $240

Number of years:45

Number of months: 45*12 = 540

Monthly interest: 0.084/12 = 0.007 or0.7%

Value at the end of 45 years = 240+240FVIFA_0.7%,539 = $1,438,259

Therefore, the amount available at the end of the 45^th year = $1,438,259