The purpose of this assignment is to solidify your understanding on the applicat
ID: 2818438 • Letter: T
Question
The purpose of this assignment is to solidify your understanding on the applications of the time value of money. The scores of this assignment will help in assessing the following learning goal of the course: “students successfully completing this course will be able to apply principles of time value of money to personal and corporate financial decisions.” Instructions: You are required to use a financial calculator or spreadsheet (Excel) to solve 10 problems (provided on page 3) on the applications of the time value of money. You are required to show the following 4 steps for each problem (sample questions and solutions are provided for guidance): (i) Develop the timeline (linear representation of the timing of cash flows) (ii) Identify the time value of money variable (PV, FV, PMT, N or Rate) which needs to be calculated in the question. (iii) Identify the values of the remaining four variables (PV, FV, PMT, N or Rate) from the question. Be sure to input positive or negative signs. (iv) Calculate the correct value of the variable identified in step (ii). Your grandparents deposit $1,000 each year on your birthday, starting the day you are born, in an account that pays 6% interest compounded annually. How much will you have in the account on your 21st birthday, just after your grandparents make their deposit? Round to two decimal places.
7. Auto Loans R Them loans you $26,000 for four years to buy a car. The loan must be repaid in 48 equal monthly payments. The annual interest rate on the loan is 9percent. What is your monthly payment? Round to two decimal places.
8. Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9 percent interest per year, how many loan payments must the company make? Round to the nearest number of periods.
9. You are ready to retire. A glance at your 401(k) statement indicates that you have $1,500,000. If the funds remain in an account earning 6.5%, how much could you withdraw at the end of each year for the next 20 years? Round to two decimal places.
10. If you wish to accumulate $280,000 in the child's college fund after 18 years, and can invest at a 7.5% annual rate, how much must you invest at the end of each year if the first deposit is made at the end of the first year? Round to two decimal places.
Explanation / Answer
(i) PMT = $ 1000, Rate = 6 % per annum compounded annually, N = 21 years and FV = ? (unknown needs to be determined)
The cash flows in the form of grand parent's deposits come in at the beginning of each time period.Hence, the total number of deposits is 22 with the first one coming in at t=0, followed by subsequent deposits at t=1,2,3,4.............21
Using a financial calculator/excel to determine the value of FV we get:
FV = 1000 x (1.06)^(21) + ..............+ 1000 x (1.06)^(1) + 1000 = $ 43392.29 (Amount accumulated in account on 21st birthday)
(ii) Loan Amount = PV = $ 26000, N = 4 years or 48 months, Rate = 9% per annum or (9/12) = 0.75 % per month, PMT = Equal Monthly Loan Repayments = ? (unknown which needs to be determined)
The monthly repayments each come in at the end of the month, thereby setting up an annuity of cash flows at t= 1 month, 2 month, 3 month ...............48 month. The sum of the present values of all these cash flows should be equal to the loan amount so as to ensure completion of the borrowing repayments.
Using a financial calculator/excel/annuity formula to solve for the unknown variable PMT, we get:
PMT = 26000 /{ [1/0.0075] x [1-(1/(1.0075)^(48))] } = $ 647.01
(iii) PV = $ 50000, PMT = $ 6202.7 and Rate = 9 % and N = ? (unknown and needs to be determined)
In this context one needs to determine the number of years over which the total present value of end of year payments of $ 6202.7 discounted at the annual interest rate would be equal to the amount borrowed.
Using financial calculator/excel/trial and error in annuity formula to determine the unknown variable N we get:
50000 = 6202.7 x [1/0.09] x [1-{1/(1.09)^(N)}]
N = 15.001 years ~ 15 years
(iv) PV = $ 1500000, N = 20 years and Rate = 6.5 %. PMT = Annual year end withdrawals = ? (unknown needs to be determined).
The annual year end withdrawals constitute a series of annuity cash flows which when discounted at the 401(k) account's interest rate and summed should be equal to the money present in the 401(k) account now(i.e $ 1500000).
Using a financial calculator/excel/annuity formula to determine the variable PMT we get:
1500000 = PMT x (1/0.065) x [1-{1/(1.065)^(20)}]
PMT = $ 136134.59
NOTE: Please raise a separate query for a solution to the last unrelated question.
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