Question

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. 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? 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?

Please show the steps you took to get the answers.

Answer 1

a) since the amount is deposited per year , it is an annuity and we have to calculate FVIFA

FVIFA = ((1+r)ⁿ-1)/r

where , r = interest rate , n = period of investment

amount accumulated in 45 years = amount deposited per year*FVIFA

b) part b is similar to part A in all respects except the period of investment

b-2) amount after 35 years = amount calculated in part b*((1+r)ⁿ)

r = interest rate , n = period of investment = 35 years

c) part c is similar to part A in all respects except the period of investment

d) for part d) you have to find interest rate per month and period of investment also in months and then the process is similar as of part a

e) amount needed for investment per year = amount required in 45 years/FVIFA