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.

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?

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?

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?

Answer 1

We have to calculate here the future value of investment of $2400 per year for 35 year @8.4% interest per year.

Formula for future value is = C x ((1+r)ⁿ-1/r

Here C = Cash flow or investment value

r = interest rate

n= total period investment

Hence = $2400 x ((1+0.084)³⁵-1)/0.084

= $2400 x 15.8277045009395/0.084= $452,220.

for 10 years return will be

$2400 x ((1+0.084)¹⁰-1)/0.084 = $2400 x 1.01005705463279/0.084 =$28,858.77

b2) if the amount is $28,858.77 is remain investment for 35 years then till will become after 35 year

formula to be for Future value = present value x (1+r)ⁿ

here present value is $28,858.77 and r =8.40% or 0.084 and n =35

Hence after 35 years the investment will become = $28,858.77 x (1+0.084)³⁵= $485,626.85

if invest $2400 for 45 years then value would become after 45 years

Future value = $2400 x ((1+0.084)⁴⁵-1)/0.084 =$107,7084.20