Write the answer of question given below related to the topic "The Time Value of Money"

4-1. You have just taken out a five-year loan from a bank to buy an engagement ring. The ring costs $5000. You plan to put down $1000 and borrow $4000. You will need to make annual payments of $1000 at the end of each year. Show the timeline of the loan from your perspective. How would the timeline differ if you created it from the bank's perspective?

4-2. You currently have a four-year-old mortgage outstanding on your house. You make monthly payments of $1500. You have just made a payment. The mortgage has 26 years to go (i.e., it had an original term of 30 years). Show the timeline from your perspective. How would the timeline differ if you created it from the bank's perspective?

4-3. Calculate the future value of $2000 in
a. Five years at an interest rate of 5% per year.
b. Ten years at an interest rate of 5% per year.
c. Five years at an interest rate of 10% per year.
d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)?

4-4. What is the present value of $10,000 received
a. Twelve years from today when the interest rate is 4% per year?
b. Twenty years from today when the interest rate is 8% per year?
c. Six years from today when the interest rate is 2% per year?

4-5. Your brother has offered to give you either $5000 today or $10,000 in 10 years. If the interest rate is 7% per year, which option is preferable?

4-6. Consider the following alternatives:
i. $100 received in one year
ii. $200 received in five years
iii. $300 received in ten years
a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year.
b. What is your ranking if the interest rate is only 5% per year?
c. What is your ranking if the interest rate is 20% per year?

4-7. Suppose you invest $1000 in an account paying 8% interest per year.
a. What is the balance in the account after 3 years? How much of this balance corresponds to "interest on interest"?
b. What is the balance in the account after 25 years? How much of this balance corresponds to interest on interest?

4-8. Your daughter is currently eight years old. You anticipate that she will be going to college in 10 years. You would like to have $100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account today to ensure that you will have $100,000 in 10 years?

4-9. You are thinking of retiring. Your retirement plan will pay you either $250,000 immediately on retirement or $350,000 five years after the date of your retirement. Which alternative should you choose if the interest rate is

a. 0% per year?
b. 8% per year?
c. 20% per year?

4-10. Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has
$3996 in it and pays an 8% interest rate.
a. How much money would be in the account if you left the money there until your 25th birthday?
b. What if you left the money until your 65th birthday?
c. How much money did your grandfather originally put in the account?

4-11. Suppose you receive $100 at the end of each year for the next three years.
a. If the interest rate is 8%, what is the present value of these cash flows?
b. What is the future value in three years of the present value you computed in (a)?
c. Suppose you deposit the cash flows in a bank account that pays 8% interest per year. What is the balance in the account at the end of each of the next three years (after your deposit is made)? How does the final bank balance compare with your answer in (b)?

4-12. You have just received a windfall from an investment you made in a friend's business. He will be paying you $10,000 at the end of this year, $20,000 at the end of the following year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year.
a. What is the present value of your windfall?
b. What is the future value of your windfall in three years (on the date of the last payment)?

4-13. You have a loan outstanding. It requires making three annual payments at the end of the next three years of $1000 each. Your bank has offered to allow you to skip making the next two payments in lieu of making one large payment at the end of the loan's term in three years. If the interest rate on the loan is 5%, what final payment will the bank require you to make so that it is indifferent between the two forms of payment?

4-14. You have been offered a unique investment opportunity. If you invest $10,000 today, you will receive $500 one year from now, $1500 two years from now, and $10,000 ten years from now.
a. What is the NPV of the opportunity if the interest rate is 6% per year? Should you take the opportunity?
b. What is the NPV of the opportunity if the interest rate is 2% per year? Should you take it now?

4-15. Marian Plunket owns her own business and is considering an investment. If she undertakes the investment, it will pay $4000 at the end of each of the next three years. The opportunity requires an initial investment of $1000 plus an additional investment at the end of the second year of $5000. What is the NPV of this opportunity if the interest rate is 2% per year? Should Marian take it?

4-16. Your buddy in mechanical engineering has invented a money machine. The main drawback of the machine is that it is slow. It takes one year to manufacture $100. However, once built, the machine will last forever and will require no maintenance. The machine can be built immediately, but it will cost $1000 to build. Your buddy wants to know if he should invest the money to construct it. If the interest rate is 9.5% per year, what should your buddy do?

4-17. How would your answer to Problem 16 change if the machine takes one year to build?

4-18. The British government has a consol bond outstanding paying £100 per year forever. Assume the current interest rate is 4% per year.
a. What is the value of the bond immediately after a payment is made?
b. What is the value of the bond immediately before a payment is made?

4-19. What is the present value of $1000 paid at the end of each of the next 100 years if the interest rate is 7% per year?

4-20. You are head of the Schwartz Family Endowment for the Arts. You have decided to fund an arts school in the San Francisco Bay area in perpetuity. Every five years, you will give the school $1 million. The first payment will occur five years from today. If the interest rate is 8% per year, what is the present value of your gift?