Ms. B is 55 years old and is planning to retire at age 62. She wants to have a r

Question

Ms. B is 55 years old and is planning to retire at age 62. She wants to have a retirement income from that point until age 85. She projects that she will need $5,000 per year during her retirement to supplement her other retirement income. In addition, she wants to leave an inheritance of $25,000 each to her four grandchildren. She has accumulated a nest egg $25,000 at this point. Assume that she can invest at a 9% annual rate in the pre-retirement period, that her funds can be invested at a 10% annual rate after retirement, and that contributions and withdrawals occur at the end of each year. If you use a financial calculator to solve, show all keystrokes and values input..

a. does she have enough accumulated at this point to fund her plan?

b. If she does not have enough, how much must she save each year for the next 7 years in order to fund her plan?

Explanation / Answer

Given information Current age = 55 Retirement age = 62 Years pending to retirement = 62 - 55 = 7 Note that it is given in question that the withdrawals are to be made at the end of each year.If I assume it to be starting from the end of 55 years it becomes 8 years till end of 62 years which is not corresponding to what is asked in Part B i.e 7 years. Hence i have calculated for 7 years Discounting rate 9 Cash flow Dsic. Cash flow 1 0 0 1 0.92 700.00 642.20 2 0.84 700.00 589.18 3 0.77 700.00 540.53 4 0.71 700.00 495.90 5 0.65 700.00 454.95 6 0.60 700.00 417.39 7 0.55 700.00 382.92 5.03 3523.07 no. of years of withdrawal after retirement = 85 - 62 = 23 23 + 7 above = 30 i.e 85 - 55 = 30 Discounting rate 10 Cash flow Dsic. Cash flow 1.00 0.00 0.00 8 0.47 5000 2332.54 9 0.42 5000 2120.49 10 0.39 5000 1927.72 11 0.35 5000 1752.47 12 0.32 5000 1593.15 13 0.29 5000 1448.32 14 0.26 5000 1316.66 15 0.24 5000 1196.96 16 0.22 5000 1088.15 17 0.20 5000 989.22 18 0.18 5000 899.29 19 0.16 5000 817.54 20 0.15 5000 743.22 21 0.14 5000 675.65 22 0.12 5000 614.23 23 0.11 5000 558.39 24 0.10 5000 507.63 25 0.09 5000 461.48 26 0.08 5000 419.53 27 0.08 5000 381.39 28 0.07 5000 346.72 29 0.06 5000 315.20 30 0.06 105000 6017.40 28523.33 Answer to A) Net present value of withdrawals to be made is 28523. The funds available today is only 25000 which is not sufficient Answer to B) Additional funds required = 28523 - 25000 = 3523 Sum of present value factors for 7 years @ 9% = 5.03 Let yearly investment be X amount Therefore 5.03X = 3523 X = 3523 / 5.03 = 700 Next 7 years amount to be invested is 700

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.