10. You have a loan outstanding. It requires making three annual payments of $10

Question

10. You have a loan outstanding. It requires making three annual payments of $1000 each at the end of the next three years. 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 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 to the two forms of payment? 11. Assume you can earn 9% per year on your investments a. If you invest $100,000 for retirement at age 30, how much will you have 35 years later for retirement? b. If you wait until age 40 to invest the $100,000, how much will you have 25 years later for retirement? c. Why is the difference so large? Perpetuities 12. You want to endow a scholarship that will pay $10,000 per year forever, starting one ear from now. If the school's endowment discount rate is 7%, what amount must you donate to endow the scholarship? How would your answer to Problem 12 change if you endow it now, but it makes the first award to a student 10 years from today? 13. 14. 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? You are offered the right to receive $1000 per year forever, starting in one year. If your discount rate is 5%, what is this offer worth to you? 15. You have $100,000 to donate to your college. You want to endow a perpetual scholar- ship that makes its first payment in 1 year. If the college's discount rate is 4%, how large will the annual scholarship payment be? 16. If you still donate the $100,000 from Problem 16 today, but ask the college to delay the scholarship payment so that the first scholarship payment is made 10 years from today, then how large will the annual payment be? 17. Annuities 18. 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? ur grandmother has been putting $1000 into a savings account on every birthday since your first (that is, when you turned one). The account pays an interest rate of 3%. How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday? 20. Assume that your parents wanted to have $160,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 8% per year on their investments a. How much would they have to save each year to reach their goal?

Explanation / Answer

10.
1000/1.05+1000/1.05^2+1000/1.05^3=x/1.05^3
=>x=1.05^3*(1000/1.05+1000/1.05^2+1000/1.05^3)
=>x=3152.5
15.
=1000/5%=20000
16.
=100000*4%=4000
20.
=(160000*0.08/(1.08^18-1-1))
=6412.763004

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