Home Work

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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 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).

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Grading Rubric

Learning

Objective

Subcomponent Not

Submitted

0

Does Not

Meet

Expectations

1

Meets

expectations

2

Exceeds Expectations

3 The student will No Attempts to Explicitly Explicitly describes make and attempt describe describes assumptions and evaluate made assumptions assumptions provides rationale on important why each assumption is assumptions in appropriate (e.g., identification of provides information appropriate time on why each time value value of money of money variable is variables FV, PV, N, I/Y or, PMT with inflows and outflows (+/- signs)

The student will Completes Completes Relevant information is convert relevant conversion of conversion of expressed in an

LO#1: The information into No information information insightful mathematical

student will be

able to apply

principles of

time value of

money to

personal and

corporate

financial

decisions.

various

mathematical

forms (e.g.,

equations,

graphs, diagrams,

tables, words)

attempt

made

but resulting

mathematical

portrayal is

inappropriate

or inaccurate

into

mathematical

portrayal

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 Calculations Calculations Calculations attempted calculate the are attempted are attempted are essentially all value of No but are both to solve the successful and unknown time attempt unsuccessful problem but sufficiently value of money made and not not comprehensive to solve variable comprehensive comprehensive 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.

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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 $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

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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 $1600 into an investment account that promises to pay a fixed interest rate of 5 percent per year. How much money will Harry

have in this account when he turns 21? Round to two decimal places.

2. At what rate must $287.50 be compounded annually for it to grow to $572.86 in 8 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 7.25% (compounded annually) in order to have $2,250 at the end of 7 years? Round to two decimal

places.

4. Biff deposited $10,000 in a bank account, and 12 years later he closes out the account, which is worth $20,000. What annual rate of interest has he earned over the

12 years? Submit your answer as a percentage and round to two decimal places.

5. How much money do you need to place into a bank account that pays a 3.2% rate in order to have $800 at the end of 6 years? Round to two decimal places.

6. 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 9 percent.

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.