Question

In: Finance

A 45 year old woman decides to place funds in a retirement plan. She can save...

A 45 year old woman decides to place funds in a retirement plan. She can save
1,550 per year and earn 6 percent on this savings. How much will she have
accumulated if she retires at age 65? If this were an annuity due, how much
extra money would she have?

Solutions

Expert Solution

We need to use the concept of Future Value of Annuity here:

where P = Periodic Payment = 1,550 per year

r = Rate of Interest per Period = 6% = 0.06

n = number of years/periods = 65-45 = 20 years

Future Value of Annuity = 1,550 x [ (1+0.06)20 - 1 ) / 0.06]

Future Value of Annuity = 1,550 x [ (1.06)20 - 1 ) / 0.06]

Future Value of Annuity = 1,550 x [ ( 3.207135 - 1 ) / 0.06]

Future Value of Annuity = 1,550 x [ 2.207135 / 0.06]

Future Value of Annuity = 1,550 x 36.78559

Future Value of Annuity = 57,017.666 = 57,017.67

She would have accumulated 57,017.67 if she retires at age 65.

If this were an annuity due

Future Value of Annuity Due = [1,550 x [ (1+0.06)20 - 1 ) / 0.06] x (1 + 0.06)

Future Value of Annuity Due = 1,550 x [ (1.06)20 - 1 ) / 0.06] x (1.06)

Future Value of Annuity Due = 1,550 x [ ( 3.207135 - 1 ) / 0.06] x (1.06)

Future Value of Annuity Due = 1,550 x [ 2.207135 / 0.06] x (1.06)

Future Value of Annuity Due = 1,550 x 36.78559 x (1.06)

Future Value of Annuity Due = 60,438.726 = 60,438.73

Extra money she would have = Future Value of Annuity Due - Future Value of Annuity

= 60,438.73 - 57,017.67 = 3,421.06

jeff jeffy answered 1 year ago
Next > < Previous

Related Solutions

Problem 7-03 A 50-year-old woman decides to put funds into a retirement plan. She can save...
Problem 7-03 A 50-year-old woman decides to put funds into a retirement plan. She can save $1,000 a year and earn 5 percent on this savings. How much will she have accumulated if she retires at age 65? Use Appendix C to answer the question. Round your answer to the nearest dollar. $ _____ At retirement how much can she withdraw each year for 20 years from the accumulated savings if the savings continue to earn 5 percent? Use Appendix...
A 20-year-old student wants to save $1000 a year for her retirement. Every year she invests...
A 20-year-old student wants to save $1000 a year for her retirement. Every year she invests $1000 in a mutual fund with an expected annual return of 8%. How much money will she have when she is 65 years old? Assume that she invests right away and did not have any money in her saving account. Part B The same student, she wants to save $100 a month instead of $1000 a year. How much money will she have when...
A 70-year-old woman has a terminal illness. She decides that she no longer wants life-sustaining measures,...
A 70-year-old woman has a terminal illness. She decides that she no longer wants life-sustaining measures, including artificial nutrition and hydration.  She is competent, understands the consequences of her actions, is not depressed, and persists in refusing treatment.  Her doctor is adamant that she cannot be allowed to die this way and her daughter, who has the healthcare power of attorney (HPOA), agrees.  The patient is prescribed 4 mg morphine IVP around the clock. (20 points each) ·        Based on the above scenario, who...
Hilda Wilde is a 45-year-old woman who was diagnosed with asthma as a child. She recalls...
Hilda Wilde is a 45-year-old woman who was diagnosed with asthma as a child. She recalls her first asthma attack being horrendous; chest tightness, difficulty breathing, wheezing, feeling anxious and sweating profusely. She was rushed to hospital and spent many days in hospital as a child until she managed to work out the triggers and control it early. The triggers for her asthma were cold temperatures, pollen, smoky environments and respiratory infections/colds, which continue to be the triggers throughout her...
Hilda Wilde is a 45-year-old woman who was diagnosed with asthma as a child. She recalls...
Hilda Wilde is a 45-year-old woman who was diagnosed with asthma as a child. She recalls her first asthma attack being horrendous; chest tightness, difficulty breathing, wheezing, feeling anxious and sweating profusely. She was rushed to hospital and spent many days in hospital as a child until she managed to work out the triggers and control it early. The triggers for her asthma were cold temperatures, pollen, smoky environments and respiratory infections/colds, which continue to be the triggers throughout her...
Mrs. Angel is a 89-year-old woman. She has a retirement pension. Her husband died a year...
Mrs. Angel is a 89-year-old woman. She has a retirement pension. Her husband died a year ago. She stays at her daughter's house. Her daughter works in a factory. Her daughter's husband, Ahmet, is an unemployed, alcoholic man with sexual problems. They have a four-year-old child. Mrs Angel is brought to the emergency unit by her daughter and Ahmet with severe abdominal pain. On physical examination, she was found to have vaginal bleeding, as well as bruises on her legs...
SECOND TOPİC: An Abuse Case Mrs. Angel is a 89-year-old woman. She has a retirement pension....
SECOND TOPİC: An Abuse Case Mrs. Angel is a 89-year-old woman. She has a retirement pension. Her husband died a year ago. She stays at her daughter's house. Her daughter works in a factory. Her daughter's husband, Ahmet, is an unemployed, alcoholic man with sexual problems. They have a four-year-old child. Mrs Angel is brought to the emergency unit by her daughter and Ahmet with severe abdominal pain. On physical examination, she was found to have vaginal bleeding, as well...
Michael is 30 years old. He comes up with a plan to save for his retirement...
Michael is 30 years old. He comes up with a plan to save for his retirement at 65 years. Currently, he has saved $40,000 in a balanced superannuation account earning 5.5% annually. He has set himself a retirement target of $2,000,000. How much must be deposited in his superannuation account starting next year each year to reach his target? Assume his contributions are to be invested at 5.5% annually. Please, round your answer to two decimal places.
A young engineer decides to save $240 per year toward retirement in 40 years. If he...
A young engineer decides to save $240 per year toward retirement in 40 years. If he invests this sum at the end of every year at 9%, then how much will be accumulated by retirement time? If by astute investing the interest rate could be raised to 12%, then what sum could be saved? If he deposits one fourth of this annual amount each quarter ($60 per quarter) in an interest bearing account earning a nominal annual interest rate of...
Alex turned 30 today, and she is planning to save $5,500 per year for retirement, with...
Alex turned 30 today, and she is planning to save $5,500 per year for retirement, with the first deposit to be made 1 year from today. She will invest in a mutual fund that will provide a return of 4% per year. She plans to retire 30 years from today, when she turns 60, and she expects to live for 30 years after retirement, to age 90. Under these assumptions, how much can she spend in each year after she...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT