Question

Stefani? German, a? 40-year-old woman, plans to retire at age? 65, and she wants to accumulate ?$430 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 5 % by investing in a? low-risk portfolio containing about 20 % ?short-term securities, 30 % common? stock, and 50 % bonds. Stefani currently has ?$41 comma 342 that at an annual rate of return of 5 % will grow to about ?$140 comma 000 by her 65th birthday? (the $ 140 comma 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 ?$20.95 each? year, she will accumulate? $1,000 by age 65. Saving 5 times that amount each? year, $ 104.75?, 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 ?$430 comma 000?? b. How much must Stefani save to accumulate the sum calculated in part a over the next 25 ?years?

Answer 1

Total Target Amount = $430,000

Current Saving = $41,342

Rate of return = 5%

Number of year = 25 year.

a.

Value of current Saving at time of retirement = $41,342 × (1 + 5%) ^ 25

= $41,342 × 3.3864

= $$139,999 or approx $140,000

Value of current Saving at time of retirement is $140,0000.

Additional money does Stefani need to accumulate = $430,000 - $140,000

= $290,000

Additional money does Stefani need to accumulate is $290,000.

b.

Annual saving  Stefani has to make to accumulate the sum is calculated in excel and screen shot provided below:

Annual saving  Stefani has to make to accumulate the sum is $6,076.21.