Question

Stefani​ German, a​ 40-year-old woman, plans to retire at age​ 65, and she wants to accumulate ​$500 comma 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 ​$34 comma 950 that at an annual rate of return of 6 % will grow to about ​$150 comma 000 by her 65th birthday​ (the $ 150, 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 ​$500,000​?

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

Answer 1

Total amount required on reaching the age of 65 years= $500,000

Future value of current savings (as given)= $150,000

Future value of savings already planned (as stated)= $5,000

Therefore,

Sub question (a): Additional amount required to be accumulated= $500,000-$150,000-$5,000= $345,000

Sub question (b): Amount to be saved every year, over 25 years in order to accumulate $345,000 is $6,288.22. These amounts are to be invested at the end of each year.

Details of calculation as follows: