Question

Decision #2: Planning for Retirement Erich and Mallory are 22, 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 $3000 per year to prepare for retirement. Mallory just told Erich, though, that she had heard that they would actually have more money the day they retire if they put $3000 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments – then they would have MORE when they retired than 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 Erich and Mallory make an informed decision: Assume that all payments are made at the END a year (or month), and that the rate of return on all yearly investments will be 7.2% annually.

Answer 1

The second investment will provide the highest amount of money.

Step-by-step explanation:

Giving the following information:

Option A:

They had been thinking that they would wait at least 10 years and then start investing $3000 per year to prepare for retirement, 35 years later.

Option B:

They put $3000 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments.

We will assume an interest rate of 10%.

For option A, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {3000*[(1.10^35)-1]}/0.10= $813,073.11

For option B, first, we need to determine the 10 years investment:

FV= {3000*[(1.10^10)-1]}/0.10= 47,812.27

Now, we calculate the 35-year investment with the following formula:

FV= PV*(1+i)^n

FV= 47,812.27*(1.10^35)= $1,343,641.30