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(solution) Exercise 1 Time Value of Money 1. A golf tournament offers the


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Exercise 1 Time Value of Money

 

1. A golf tournament offers the following prizes for the champion of the

 

competition:

 

a.

 

Payment of $2,000,000 cash at the end of the game

 

b.

 

Payment of $3,500,000 cash at the end of 5 years

 

c.

 

Payment of $350,000 per year for the next 10 years

 

d.

 

Payment of $200,000 per year forever

 

e.

 

Payment of $300,000 per year forever, from the beginning of 5th year

 

If the annual interest rate is 10%, which award will be the best?

 

e. PV=$2,253,944

 

2. Irina is 25 years old this year, and will complete her master degree at the end of

 

this year. She is expected to start her full-time job at the beginning of next year,

 

and she plans to retire at the end of the 30th year of her work (at the age of 55).

 

Her annual income for the next year will be $50,000. Her annual income will

 

grow 5% per year until she becomes 55 years old. The interest rate is 10% per

 

year.

 

a. What will be the present value of all her income until she retires?

 

$752,316

 

b. If Irina saves 5% of her annual income and makes annual deposit which

 

gives 10% interest rate, what will be the total amount she can withdraw

 

from her savings at the year she retires?

 

$656,373

 

c. Instead of receiving the money at a lump-sum, Irina decides to receive the

 

money as annual equal payments for the next 20 years from the age of 56

 

until 75 years old. How much will be the annual payment?

 

$77,097

 

3. Irina?s bank deposit balance is $1 million. She will need to withdraw $500,000

 

next year, but she will be able to make another deposit of $100,000 at the end of

 

the second year. She needs annuity payments of three years from the end of the

 

third year until the end of the fifth year. Assuming the interest rate on her deposit

 

is 10%, how much will be her annuity payments during the year 3-5?

 

$305,607.19

 


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