A woman is retiring in January at the age of 65 and has three options for receiv

Question

A woman is retiring in January at the age of 65 and has three options for receiving the proceeds from a tax-free retirement annuity. She can either: A. Receive an immediate lump-sum payment of $30,976; B. Receive payments of $359.60 per month for the rest of her life; or C. Receive payments of $513.80 per month for the next 10 years. With option B, the payments will stop at the time of death: with C, however, the payments will continue for 10 years, with payments going to the woman's heirs if she dies before all payments are made). (a) Assuming that the woman uses an interest of 9% in making financial decisions, develop a table that shows the equivalent annual income for each alternative as a function of the age at which she will die. (Assume that the woman will not live past age 100.) Use your result from part (a) to develop a choice table that shows which alternative would be best as a function of the age at which the woman dies. (b) c) According to the US Social Security Administration, a woman reaching age 65 today can expect to live, on average, until age 86.6. Assuming the woman dies at the age expected, which is best alternative?

Explanation / Answer

Expected life 100 years A. If She receive 39,976 then till the age of 100 she get $242.85 per month Principal                 30,976 Rate of Interest 9% 0.75% Per Month Years 35 420 months Monthly Mortgage Payment= =(30976*.75%*(1+.75%)^420)/((1+.75%)^420-1)       242.85 B. Receive 359.60 per month       359.60 C. Receive 513.80 per month for next 10 years Additional Money Receives 513.8-359.6=154.20 Future Value of 154.20 received monthly after 10 years FV = P * {(((1+R)^N) - 1) / R} P       154.20 R 0.75% N 120 Months =154.20*((((1+.75%)^120)-1)/.75%)              29,840 Principal                 29,840 Rate of Interest 9% 0.75% Per Month Years 25 300 months Monthly Mortgage Payment= =(29840*.75%*(1+.75%)^300)/((1+.75%)^300-1)       250.42 So if She adopt option C and lives upto 100 years than first 10 years she can enjoy 359.60 per month but next 25 years she will get 250.42 per month Conclusion: Option B receive till whole life 359.60 is best (life is assumed to be 100 years) (c ) expected life 86.6 Years If She receive 39,976 then till the age of 86.6 she get $242.85 per month Principal                 30,976 Rate of Interest 9% 0.75% Per Month Years (86.6-65) 21.6 259.2 months Monthly Mortgage Payment= =(30976*.75%*(1+.75%)^259.2)/((1+.75%)^259.2-1)       271.46 B. Receive 359.60 per month       359.60 C. Receive 513.80 per month for next 10 years Additional Money Receives 513.8-359.6=154.20 Future Value of 154.20 received monthly after 10 years FV = P * {(((1+R)^N) - 1) / R} P       154.20 R 0.75% N 120 Months =154.20*((((1+.75%)^120)-1)/.75%)              29,840 Principal                 29,840 Rate of Interest 9% 0.75% Per Month Years (86.6-(65+10)) 11.6 139.2 months Monthly Mortgage Payment= =(29840*.75%*(1+.75%)^139.2)/((1+.75%)^139.2-1)       346.13 So if She adopt option C and lives upto 86.6 years than first 10 years she can enjoy 359.60 per month but next 11.6 years she will get 346.13 per month Conclusion: Option B receive till whole life 359.60 is best (life is assumed to be 86.6years)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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