Calculating
a. If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?
b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit?
c. Suppose your friend’s employer will contribute $3,500 to the account every year as part of the company’s profit-sharing plan. In addition, your friend expects a $175,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?
a)
To calculate: The required savings for each year
Introduction:
The series of payments that are made in equal intervals is an annuity payment. The amount of annuity payments is mainly calculated based on the particular situation.
Answer to Problem 68QP
The required savings for each year is $11,776.01
Explanation of Solution
Given information:
Person X’s friend is celebrating her 35th birthday today as she wishes to start saving for her retirement at the age of 65. She wants to withdraw a sum of $105,000 on each of her birthdays for 20 years that is followed by her retirement in which, the first withdrawal will fall on her 66th birthday. She also intends to put her money in the local credit union that offers a 7% interest for a year. She also wishes to make equivalent annual payments on each of her birthdays into the account that is established at the Credit Union for retirement fund.
It is assumed that she starts making the deposit on her 36th birthday and continues to make it until her 65th birthday.
Timeline of the amount that is necessary for retirement is as follows:
Note: In the above given information, every question is asked for a different cash flow but it is for the funding of the same retirement plan. Each of the saving possibility has the similar future value that refers to the present value of the spending on the retirement when Person X’s friend is ready for the retirement.
Formula to calculate the present value annuity is as follows:
Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. Thus, by the present value of annuity, the amount that is essential for Person X’s friend is when she is ready for the retirement and it can be calculated as follows:
Compute the present value annuity:
Hence, the amount that is required for Person X’s friend at the time of retirement is $1,112,371.50
Note: The present value of annuity is same for all the necessary requirements.
The timeline that denotes when Person X’s friend makes equivalent annual deposits into the account and with the future value of annuity equivalent to the sum essential at the time of retirement is as follows:
Formula to calculate the future value annuity is as follows:
Note: C denotes the annual cash flow or annuity payment, r denotes the rate of interest, and t denotes the number of payments. The future value of annuity represents the necessary savings for each year.
Compute the future value annuity:
Hence, the required savings for each year is $11,776.01.
b)
To calculate: The present value of the lump sum savings
Introduction:
The series of payments that are made in equal intervals is an annuity payment. The amount of annuity payments is mainly calculated based on the particular situation.
Answer to Problem 68QP
The present value of the lump sum savings is $146,129.04
Explanation of Solution
Given information:
Person X’s friend is celebrating her 35th birthday today as she wishes to start saving for her retirement at the age of 65. She wants to withdraw a sum of $105,000 on each of her birthdays for 20 years that is followed by her retirement in which, the first withdrawal will fall on her 66th birthday. She also intends to put her money in the local credit union that offers a 7% interest for a year. She also wishes to make equivalent annual payments on each of her birthdays into the account that is established at the Credit Union for retirement fund.
Person X’s friend has just inherited a large sum of money. She decides to make the lump sum payment on her 35th birthday to cover the needs of retirement rather than making equal annual payments.
Timeline for the lump sum saving amount is as follows:
Formula to compute the future value is as follows:
Note: C denotes the annual cash flow or annuity payment, r denotes the rate of interest, and t denotes the number of payments.
Compute the future value:
Hence, the lump sum amount is $146,129.04
c)
To calculate: The annual contribution of Person X’s friend
Introduction:
The series of payments that are made in equal intervals is an annuity payment. The amount of annuity payments is mainly calculated based on the particular situation.
Answer to Problem 68QP
The annual contribution of Person X’s friend is $4,631.63
Explanation of Solution
Given information:
Person X’s friend is celebrating her 35th birthday today as she wishes to start saving for her retirement at the age of 65. She wants to withdraw a sum of $105,000 on each of her birthdays for 20 years that is followed by her retirement in which, the first withdrawal will fall on her 66th birthday. She also intends to put her money in the local credit union that offers a 7% interest for a year. She also wishes to make equivalent annual payments on each of her birthdays into the account that is established at the Credit Union for retirement fund.
The employer of Person X’s friend contributes a sum of $3,500 into her account each year as a part of sharing the profit. In addition, Person X’s friend also expects a sum of distribution from her family trust on her 55th birthday that amounts to $175,000.
Timeline of the lump sum saving in addition to the annual deposit is as follows:
Note: The value that is essential for retirement is known as the value of the lump sum saving at retirement can be subtracted to determine how much Person X’s friend is short of.
Formula to compute the future value of the trust fund deposit is as follows:
Note: C denotes the annual cash flow or annuity payment, r denotes the rate of interest, and t denotes the number of payments.
Compute the future value of the trust fund deposit is as follows:
Hence, the future value of the trust fund deposit is $344,251.49.
The amount that Person X’s friend needs at retirement is calculated as follows:
Hence, the amount that Person X’s friend needs at the time of retirement is $768,120.01.
Note: The payment can be solved by using the equation of the future value of annuity.
Formula to calculate the future value annuity is as follows:
Note: C denotes the annual cash flow or annuity payment, r denotes the rate of interest, and t denotes the number of payments.
Compute the future value annuity:
Hence, the total annual contribution is $8,131.63
Compute the contribution that is made by Person X’s friend is as follows:
Note: The contribution made by Person X’s friend is calculated by subtracting the employer’s contribution from the total annual contribution.
Hence, the contribution made by Person X’s friend is $4,631.63.
Want to see more full solutions like this?
Chapter 6 Solutions
Fundamentals of Corporate Finance
- Excel Master It! Problem This is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals: Years until retirement: 30 Amount to withdraw each year: $90,000 Years to withdraw in retirement: 20 Interest rate: 8% Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund. If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement? Suppose your friend just inherited a large sum of money. Rather than making equal annual payments, she decided to make one lump-sum deposit today to cover her retirement needs. What amount does she have to deposit today? Suppose…arrow_forward1. Your financial planner has advised you to initiate a retirement account while you are still young. Today is your 35th birthday and you are planning to retire at age 65. Actuarial tables show that individuals in your age group have a life expectancy of about 75. If you want a $50,000 annuity beginning on your 66th birthday which will grow at a rate of 4 percent per year for 10 years: a. What amount must you deposit at the end of each year through age 65 at a rate of 8 percent compounded annually to fund your retirement account? b. How would your answer change if the rate is 9 percent? ¢. After you have paid your last installment on your 65th birthday, you learn that medical advances have shifted actuarial tables so that you are now expected to live to age 85. Determine the base-year annuity payment supportable under the 4 percent growth plan with a 9 percent interest rate.arrow_forwardThis is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retire- ment spending goals: Years until retirement: Amount to withdraw each year: Years to withdraw in retirement: Interest rate: 30 $90,000 20 8% Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund. a. If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement?arrow_forward
- You are saving for retirement. To live comfortably, you decide that you will need $2.5 million by the time you are 65. Today is your 30th birthday, and you decide, starting today, and on every birthday up to and including your 65th birthday, that you will deposit the same amount into your savings account. Assuming the interest rate is 5%, the amount that you must set aside each year on your birthday is closest to: O $71,430. O $26,260. O $26,100. O $27,680.arrow_forward39. Problem 5.39 (Required Annuity Payments) 19 Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $45,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 4%. He currently has $235,000 seved, and he expects to earn 916 annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round intermediate calculations. Round your answer to the nearest dollar $arrow_forwardYou are saving for retirement. To live comfortably, you decide you will need to save $1 million by the time you are 65. Today is your 31st birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 9%, how much must you set aside each year to make sure that you will have $1 million in the account on your 65th birthday? $0 The amount to deposit each year is $ (Round to the nearest dollar.) et more help Clear allarrow_forward
- You are saving for retirement. To live comfortably, you decide you will need to save $2,500,000 by the time you are 65. Today is your 32nd birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 7%, how much must you set aside each year to make sure that you will have $ 2,500,000 in the account on your 65th birthday? The amount to deposit each year must be $arrow_forward. Problem 5.03 (Finding the Required Interest Rate) еВook Your parents will retire in 16 years. They currently have $400,000 saved, and they think they will need $2,100,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.arrow_forwardAssume that Social Security promises you $43,000 per year starting when you retire 45 years from today (the first $43,000 will get paid 45 years from now). If your discount rate is 5%, compounded annually, and you plan to live for 17 years after retiring (so that you will receive a total of 18 payments including the first one), what is the value today of Social Security's promise? ... The value today of Social Security's promise is $ the nearest cent.) (Round toarrow_forward
- Your friend is celebrating her birthday and wants to start saving for retirement. She has provided you with the following information: Years until retirement: 30 Amount to withdraw each year in retirement: $120,000 Years to withdraw in retirement: 12 Interest rate while saving: 9% Interest rate in retirement: 6% Saved today (nest egg): $25,000 The first deposit will be made one year from today, and the last deposit will be made on the day she retires. Her first withdrawal will not occur until one year after she retires, and she plans to spend her entire nest egg. Calculate the amount she must deposit each year to reach her retirement goal. (Round to 2 decimals)arrow_forward13. You have just made your first $4,000 contribution to your retirement account. Assuming you earn an 11 percent rate of return and make no additional contributions, what will your account be worth when you retire in 45 years? What if you wait 10 years before contributing? (Does this suggest an investment strategy?). 14. You are saving up for a down payment on a house. You will deposit $600 a month for the next 24 months in a money market fund. How much will you have for your down payment in 24 months if the fund earns 12% APR compounded monthly?arrow_forwardYou are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 26th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 4%, how much must you set aside each year to make sure that you will have $2 million in the account on your 65th birthday?arrow_forward
- Essentials Of InvestmentsFinanceISBN:9781260013924Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.Publisher:Mcgraw-hill Education,
- Foundations Of FinanceFinanceISBN:9780134897264Author:KEOWN, Arthur J., Martin, John D., PETTY, J. WilliamPublisher:Pearson,Fundamentals of Financial Management (MindTap Cou...FinanceISBN:9781337395250Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage LearningCorporate Finance (The Mcgraw-hill/Irwin Series i...FinanceISBN:9780077861759Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan ProfessorPublisher:McGraw-Hill Education