AFF 502, Problem Set Number Two November 4th, 2022 (1)

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Toronto Metropolitan University *

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502

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Finance

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Feb 20, 2024

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AFF 502 P ROBLEM S ET T WO S TUDENT N AME ____________________S TUDENT N UMBER ________________________ S TUDENT N AME ____________________S TUDENT N UMBER ________________________ S TUDENT N AME ____________________S TUDENT N UMBER ________________________ P LEASE NOTE THE FOLLOWING :  If you make any assumptions to solve the problem, clearly state them at the beginning of the solution and explain the reason.  The problem set is to be done individually or in a group of no more than 3 students.  You are to hand in an electronic copy of the assignment on the D2L Class page. Only one member of the group needs to submit the hard copy however the first worksheet in your workbook must clearly state the names, student numbers and section number of all of the group members.  You do not to use formulatext to show your work, however I must be able to click on the various cells in your worksheet and see the formula or function you have used to solve a particular part of the problem.  This assignment is due at 11:59 pm on November 27 th , 2022 1

Q UESTION O NE : YOUR SISTERS ’ M ORTGAGES (30 MARKS ) Your sisters Rebecca and Debra each just bought a house. Each sister paid $1,150,000 for the house. Each sister had a down payment of $300,000. Each sister got a mortgage with a 3-year term and a 25 amortization period. The rate on each mortgage was 5.2% compounded semi-annually. Payments will be made weekly. 1) What is the amount of the Rebecca’s weekly payment? 2) How much will Rebecca pay in interest during the 1 st payment after the term has ended? The amount of interest paid in payment number 157. 3) Rebecca plans on making her required weekly payment during the life of the mortgage. How much will she owe on the mortgage at the end of the term? 4) How many years until Rebecca has paid off her mortgage? 5) How much will Rebecca pay in interest over the life of the mortgage? 6) Debra has decided to increase her weekly payments by $150 per week. She plans on making the increased payments until her mortgage is paid off. What is the amount of Debra’s weekly payment? 7) How much will Debra pay in interest during the 1 st payment after the term has ended? The amount of interest paid in payment number 157. 8) How much will Debra owe on the mortgage at the end of the term? 9) Debra will keep making the extra payment until she has paid off her mortgage. How many years will it take Debra to pay off her mortgage? 10) How much will Debra pay in interest over the life of the mortgage? After you have answered the questions above you are to create the following array (box) in the excel sheet that contains the answers. Rebecca Debra Amount of Weekly Payment? Amount of interest paid in payment 157? How much is owing on mortgage at the end of the term? How many years until the mortgage is paid off? How much interest was paid over the life of the mortgage? 2

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P ROBLEM 2: R ETIREMENT P LANNING FOR YOUR O THER S IBLINGS ’ R ETIREMENT (30 MARKS ) Your 4 siblings Maya, Kadeisha, Samuel and Tesho are all 22 years old. Each of them plans on retiring in 45 years. They have already determined the amount of money they need at retirement. These amounts are shown in the table below: Maya Kadeisha Samuel Tesho Amount Needed $3,500,000 $3,500,000 $3,500,000 $3,500,000 Once you have determined the answers to the questions below you should insert and complete the following array (box) on your excel sheet. Maya Kadeisha Samuel Tesho Amount of annual payment Maya has decided to start saving for retirement immediately. She will make an annual contribution into her retirement account. The contribution will be made at the end of each year. She expects to earn 6.5% compounded annually prior to retirement. What is amount of her annual contribution? Samuel has decided to start saving for retirement immediately. He will make an annual contribution into his retirement account. The contribution will be made at the end of each year. He expects to earn 6.5% compounded annually prior to retirement. After the initial contribution Samuel plans on increasing his annual contributions by 3% each year. What is the amount of his initial contribution? Kadiesha has decided to postpone saving for her retirement. Her plan is to make her first contribution to her retirement account when she turns 43, which will be 21 years from today. She will make a total of 25 annual contributions to the account. She expects to earn 6.5% compounded annually prior to retirement. The contributions will be made at the end of the year. What is amount of her annual contribution? Tesho has decided to postpone saving for his retirement. His plan is to mark his first contribution to his retirement account when he turns 43, which will be 21 years from today. He will make a total of 25 annual contributions to the account. The contribution will be made at the end of each year. He expects to earn 6.5% compounded annually prior to retirement. The first contribution to his retirement account will be made 21 years from today. After the initial contribution Samuel 4

plans on increasing his annual contributions by 3% each year. There will be a total of 25 annual contributions to the account. What is the amount of his initial contribution? 5

P ROBLEM 3: D EFINED B ENEFIT P ENSION PLANS (30 MARKS ) You have 2 sisters, Chrystia and Melanie. Your sisters are 40 years old. Your sisters wish to retire when they are 60 years old. Each of your sisters expect to live for 40 years after they retire. Each sister will receive a total of 40 annual payments from their pension. Chrystia and Melanie belong to a defined benefit pension plan. Chrystia’s defined benefit pension plan will pay her 2% for each year she has worked at her company. Chrystia has worked for her current employer for 10 years. She expects to work for her current employer until she retires in 20 years. Her annual pension will be based on her average annual salary during her last 5 years of work. The calculation is the number of years worked * 2% * average annual salary during her last 5 years of work. She currently is being paid $70,000 per year. For simplicity you may assume that the current salary is being paid at the beginning of the year. She expects her salary to increase by 3% per year. There will be a total of 19 salary increases. During retirement she will receive an annual income from her pension plan. The annual pension payments will be made at the beginning of each year. She will receive a total of 40 pension payments. Her annual pension payments will increase by the rate of inflation. Chrystia expects inflation to be 3% per year during retirement. Melanie’s defined benefit pension plan will pay her 2% for each year she has worked at her company. Melanie has worked for her current employer for 5 years. She expects to work for her current employer until she retires in 20 years. Her annual pension will be based on her average annual salary during her last 5 years of work. The calculation is the number of years worked * 2% * average annual salary during her last 5 years of work. She currently is being paid $60,000 per year. For simplicity you may assume that the current salary is being paid at the beginning of the year. She expects her salary to increase by 2% per year. There will be a total of 19 salary increases. During retirement she will receive an annual income from her pension plan. The annual payments will be made at the beginning of each year. She will receive a total of 40 pension payments. Melanie’s pension plan is not indexed, her annual payments will not change. Chrystia and Melanie’s employers believe that after retirement the pension plans will earn an effective annual rate of return of 5%. Prior to retirement the pension plans will earn an effective annual rate of return of 6%. 6

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Part A: 1) What was the amount of Chrystia’s final year’s annual salary? 2) What was the average salary during Chrystia’s final five years of working? 3) What is the amount of Chrystia’s first annual pension payment? 4) What is the amount of Chrystia’s final annual pension payment? 5) How much money will Chrystia’s employer need to have when Chrystia retires to make the anticipated annual pension payments to Chrystia? 6) Assuming the Chrystia’s employer decides to set up an annuity to fund Chrystia’s pension payments after she retires, how much must the employer contribute to the annuity every year? There will be a total of 20 annual contributions to the annuity, and the contributions will be made at the end of each year. 7) What was the amount of Melanie’s final year’s annual salary? 8) What was the average salary during Melanie’s final five years of working? 9) What is the amount of Melanie’s first annual pension payment? 10) What is the amount of Melanie’s final annual pension payment? 11) How much money will Melanie’s employer need to have when Melanie retires to make the anticipated annual pension payments to Melanie? 12) Assuming the Melanie’s employer decides to set up an annuity to fund Melanie’s pension payments after she retires, how much must the employer contribute to the annuity every year? There will be a total of 20 annual contributions to the annuity, and the contributions will be made at the end of each year. On your excel sheet you should create an array (box) where you fill in the answers to the above questions. Chrystia Melanie Amount of final year’s salary? Average salary during final five years of work? Amount of first annual pension payment? Amount of final annual pension payment? Amount needed by employer to fund anticipated pension payments? Amount of annual contribution (payment) the 7

employer needs to make for the next 20 years to fund the pension? 8

P ROBLEM 4: PROBABILITY OF A P ERSON W HO JUST TURNED 22 L IVING TO A G IVEN A GE (10 MARKS ) Using the standard mortality tables posted on the class page, you are to complete the following table. What is the probability of person who just turned 22 living to a given age? Age Probability of Male Living to Probability of Female Living to 70 75 80 85 90 95 100 9

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