Question

Stefani​ German, a​ 40-year-old woman, plans to retire at age​ 65, and she wants to accumulate ​$440,000 over the next 25 years to supplement the retirement programs that are being funded by the federal government and her employer. She expects to earn an average annual return of about 6% by investing in a​ low-risk portfolio containing about 20% ​short-term securities, 30% common​ stock, and 50% bonds. Stefani currently has ​$27,960 that at an annual rate of return of 6% will grow to about ​$120,000 by her 65th birthday​ (the $120,000 figure is found using time value of money​ techniques, Chapter 4​ Appendix.) Stefani consults a financial advisor to determine how much money she should save each year to meet her retirement savings objective. The advisor tells Stefani that if she saves about ​$18.23 each​ year, she will accumulate​ $1,000 by age 65. Saving 5 times that amount each​ year, $91.15​, allows Stefani to accumulate roughly​ $5,000 by age 65.

a. How much additional money does Stefani need to accumulate over time to reach her goal of ​$440,000​?

b. How much must Stefani save to accumulate the sum calculated in part a over the next 25 ​years?

Answer 1

a) How much additional money required.

She wants to accumulate amount = 440000

She already has $27960 which becomes 120000 at time 65 as given in question.

So additional amount required to acumulate = 440000 -120000 = 320000

b) How much to save per year over 25 years to accumulate = 320000

It is given in the question that saving $18.23 each year will result in accumulation of $1000 over 5 years.So if you want to save 320000 that you need to save each year as:

= (320000 / 1000) x 18.23

= 320 x 18.23

= 5833.6

$5833.6 each year saving and deposit will lead you to accumulate 320000 in 25 years.