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# 2. (15 points) Suppose that you are thinking to buy an annuity that

pays \$1,000 every month from the end of October 2020 to the end of September 2025. The quoted annual rate is 4%. (a) (5 points) How much are you willing to pay for it on October 1, 2020? (b) (5 points) How much will you be willing to pay a year later? (c) (5 points) From the perspective of October 1, 2020, what is the future value of all payments at the end of September 2025? At the end of March 2026?

3. (10 points) Suppose that the UK decides to renew its old tradition and starts to issue perpetual bonds again. Assume that such a bond promises to pay you £100 annually. The current interest rate is 2%. (a) (4 points) How much will you be willing to pay for such a bond? 1 (b) (4 points) Suppose now that annual payments are linked to the growth of the UK economy. In particular, the UK government thinks that it will grow at 1% rate indefinitely, so it promises to increase annual bond payments by 1% every year (the first payment is still £100). What is the price of the bond then? (c) (2 points) Suppose now that the UK government promises to increase the annual payments at 2% per year. How will your answer change then? Do you think this promise can be kept?

4. (10 points) According to WSJ, friends and relatives of young Warren Buffet regularly heard him complaining that he did not want to spend \$300,000 for his haircut. Back in the day, a haircut would cost Mr Buffet around \$0.5. For how long do you need to compound the haircut price to justify Mr Buffet's complaints? Give answers assuming that interest rate is 1%, 5%, and 10%. What if you use simple interest rate?

5. (15 points) You have \$100 and think where to invest your money. You have three options. Option A promises you a weekly interest rate of 0.3%, compounded weekly. Option B promises a 16% annual interest rate with one payment at the end of each year. Finally, option C has a quoted annual rate of 15% with quarterly compounding. Assume that a year consists of 52 weeks. (a) (3 points) What are APRs of the three investment opportunities? (b) (6 points) Rank these investment opportunities by their attractiveness to you. (c) (6 points) How much more will earn over 10 years if you invest in your most preferable option relative to your least preferable option?

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2. (15 points) Suppose that you are thinking to buy an annuity that pays \$1,000 every month from the end of October 2020 to the end of September

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