Question

Decision #2: Planning for Retirement Evan and Gina 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 $2700 per year to prepare for retirement. Gina just told Evan, though, that she had heard that they would actually have more money the day they retire if they put $2700 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 Evan and Gina 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. (Please do NOT ROUND when entering "Rates" for any of the questions below)

Answer 1

Value of an Annuity:

An annuity refers to a series of uniform cash flows that occur at the start or the end of a regular time interval. An annuity that occurs at the start of a period is referred to as an annuity due while that which occurs at the end of the period is an ordinary annuity. The present value or future value of an annuity is calculated based on the concept of the time value of money which states that a dollar today is worth more than a dollar in the future.

Answers for the above given two questions are as follows;

d)

Annuity = $225

n = 45 adjusted for monthly compounding 45 *12 =540 months

APR =7.2% adjusted for monthly compounding = 0.072/12 =0.006

(1 + r)" - 1 FVOA = Annuity * r

= 225 * (((1+0.006)^540-1)/0.006))

= 910789.31

Evan and Gina will have $910789.31 in 45 years if they put away $225 per month at the end of each month for the next 45 years.

e)

n = 20 years

APR =7.2%

FV = $1,000,000

(1 + r)" - 1 FVOA = Annuity * r

1000000 = Annuity * (((1+ 0.072)^20-1)/0.072)

1000000 = Annuity * 41.90

Annuity = 1000000 / 41.90

= 23866.35

To achieve the goal of saving $1,000,000 in 20 years, Evan and Gina will have to save $23,866.35 per year.