At what rate must $287.50 be compounded annually for it to grow to $650.01 in 14 years?

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ASSIGNMENT #1

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 4) 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).

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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 $600,000 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

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(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%

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Assignment Problems

1. On the day Harry was born, his parents put $1200 into an investment account that promises to pay a fixed interest rate of 6 percent per year. How much money will Harry have in this account when he turns 21 (round to nearest $1)?

2. At what rate must $287.50 be compounded annually for it to grow to $650.01 in 14

years?

3. How much money must be put into a bank account yielding 6.42% (compounded annually) in order to have $1,671 at the end of 11 years (round to nearest $1)?

4. Biff deposited $9,000 in a bank account, and 10 years later he closes out the account,

which is worth $18,000. What annual rate of interest has he earned over the 10 years?

5. How much money do I need to place into a bank account that pays a 1.08% rate in order to have $500 at the end of 7 years (round to nearest $1)?

6. Your grandparents deposit $2,000 each year on your birthday, starting the day you are

born, in an account that pays 7% interest compounded annually. How much will you have in the account on your 21st birthday, just after your grandparents make their deposit (round to nearest $1)?

7. Auto Loans R Them loans you $24,000 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 9 percent. What is the monthly payment (round to nearest $1)?

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 nearest $1)?

9. You are ready to retire. A glance at your 401(k) statement indicates that you have

$750,000. If the funds remain in an account earning 9.0%, how much could you withdraw at the beginning of each year for the next 25 years (round to nearest $1)?

10. If you wish to accumulate $200,000 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 nearest $1)?

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Grading Rubric

Learning Objective Subcomponent Not Submitted

0

Does Not Meet Expectations

1

Meets expectations

2

Exceeds Expectations

3 LO#1: The student will be able to apply principles of time value of money to personal and corporate financial decisions.

The student will make and evaluate important assumptions in identification of appropriate time value of money variables

No attempt made

Attempts to describe assumptions

Explicitly describes assumptions

Explicitly describes assumptions and provides rationale on why each assumption is appropriate (e.g., provides information on why each time value of money variable is FV, PV, N, I/Y or, PMT with inflows and outflows (+/- signs)

The student will convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, tables, words)

No attempt made

Completes conversion of information but resulting mathematical portrayal is inappropriate or inaccurate

Completes conversion of information into mathematical portrayal

Relevant information is expressed in an insightful mathematical portrayal in a way that contributes to a further or deeper understanding (e.g., correctly develops timeline of cash flows by labeling FV, PV, N, I/Y and PMT as time value of money variables)

The student will calculate the value of unknown time value of money variable

No attempt made

Calculations are attempted but are both unsuccessful and not comprehensive

Calculations are attempted to solve the problem but not comprehensive

Calculations attempted are essentially all successful and sufficiently comprehensive to solve the problem. Calculations are also presented elegantly (e.g., provides information on the interpretation of the calculated time value of money variable such as the calculated PMT means annuity)

The above rubric will be applied to grade each question and the average score will be calculated for each subcomponent.