he 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).

Sample Questions and Solutions Sample Question1: Sara wants to have $100,000 in her savings account after 6 years. How much must she put in the account now, if the account pays a fixed interest rate of 8%, to ensure that she has $100,000 in 6 years?

Solution:

(i) Develop the timeline: Years 0 1 2 3 4 5 6 Cash Flows ? 0 0 0 0 0 $100000

(ii) Time Value of Money Variable which needs to be calculated: Present Value (PV) Rationale: The question is how much she should put now. This unknown value is as of today (now) and therefore represented by the Present value.

(iii) Values of the remaining four variables: FV = $100,000; N= 6 years; Rate = 8%; PMT = 0 Rationale: She wants $100,000 after 6 years. This amount is expected to occur in the future and therefore is represented by the Future value. The investment duration is 6 years and therefore it the N. She expects to earn 8% therefore it is the Rate. There is no annuity amount and therefore PMT is zero.

(iv) Calculation: FV = $100,000; N= 6 years; Rate = 8%; PMT = 0; Calculate PV = $63,016.96 Amount she should put in the account today: $63,016.96. Sample Question2: Anthony borrowed $50,000 today that he must repay in 15 annual end-of-year installments of $5,000. What annual interest rate is Anthony paying on his loan?

Solution:

(i) Develop the timeline: Years 0 1 2 3 4 5 6 Cash Flows -$50,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 Years 7 8 9 10 11 12 13 Cash Flows $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 Years 14 15 Cash Flows $5,000 $5,000

(ii) Time Value of Money Variable which needs to be calculated: Rate (I/Y) Rationale: The question is how much annual interest rate she is paying. This unknown variable is represented by Rate.

(iii) Values of the remaining four variables: PV = -$50,000; N= 15 years; PMT = $5,000 FV = 0 Rationale: She has borrowed $50,000 as of today. Therefore, this is the present value. The time duration of the loan s 15 years, and therefore it is N. The annual payment which is required to be paid is $5,000. This is the annuity since same amount is paid every year and therefore represented by the PMT. The value of the loan at the end of the loan period is expected to be zero. Therefore, the future value is zero.

(iv) Calculation: PV = -$50,000; N= 15 years; PMT = $5,000 FV = 0; Calculate I/Y = 5.56% Interest rate she is paying: 5.56%

Assignment Problems 1. On the day Saffron was born, her parents put $36,000 into an investment account that promises to pay a fixed interest rate of 11 percent per year. How much money willshe have in this account when she turns 18? Round to two decimal places.

2. At what rate must $400 be compounded annually for it to grow to $900.88 in 12 years? Submit your answer as a percentage and round to two decimal places.

3. How much money must be put into a bank account yielding 5.25% (compounded monthly) in order to have $6,800 at the end of 11 years? Round to two decimal places.

4. Yolanda deposited $8,000 in a bank account, and 9 years later she closes out the account, which is worth $16,000. What annual rate of interest has she earned over the time period? Submit your answer as a percentage and round to two decimal places. 5. Bridgette wants to retire 41 years from now. She decides to start saving $350 each month into a Roth IRA starting at the end of this month. If the IRA is expected to earn an average annual return of 13% compounded monthly, how much will she have in the account at the end of 41 years? Round to two decimal places.

6. Durran has recently acquired a rare art piece that he plans to put on display in his private collection. He estimates that revenues generated from donations and admissions tickets to see the new exhibit will be $23,000 per year for the next five years. If he requires a rate of return of 7%, how much are the expected cash flows worth for him today? Round to two decimal places.

7. Your uncle Adelai promises to pay you $16,000 in five years. You believe that you can earn a 6% rate of return on any investments made between now and then. How much is the amount worth to you today? Round to two decimal places.

8. Your company has received a $75,000 loan from an industrial finance company. The annual payments are $14,058.30. If the company is paying 10 percent interest per year, how many loan payments must the company make? Round to the nearest number of years.

9. You are ready to retire. A glance at your 401(k) statement indicates that you have $2,800,000. If the funds remain in an account earning 5% annually, how much could you withdraw at the end of each year for the next 25 years? Round to two decimal places.

10. If you wish to accumulate $380,000 in your child's college fund after 18 years and can invest at a 9% 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.