1. You just won the lottery! Congratulations! The jackpot total was $35 million after taxes. According to the payout scheme, you will receive $10 million today (meaning right now) and $5 million each year for the next 5 years. What is the present value of this lottery jackpot when the interest rate is 3.5%?
2. The Tyrell Corporation is seeking to increase capital to invest in its new line of android-workers, Nexus 6. To accomplish this, they are selling $125,000-face-value bonds with a 10% coupon rate at a current price of $90, 000.
(a) What is the current yield on the bond?
(b) If the price of these bonds are expected increase to $95, 000 in the nest year, what is the expected rate of capital gains/losses?
(c) What is the expected rate of return?
3. Suppose you purchase a U.S. Treasury Bond with a face-value of $2, 500 and a 10-year maturity for a price of $1, 000.
(a) What is the yield-to-maturity on this bond?
(b) If the interest rate were to decrease by 1% in the second year of holding the bond, what is the new price of the U.S. Treasury bond?
(c) Given the above answer, what is the capital gain/loss if you were to sell the bond in year 2?
4. You just deposited $3, 500 into a bank account and the current real interest rate is at r = 2% and inflation is expected to be ?e = 3% over the next year.
(a) What nominal interest rate, i, from the bank would you require?
(b) How much money will you have at the end of one year?
(c) How much money will you have at the end of two years?
(d) If you are saving up to buy a used car in three years that will cost you $4, 025; will you have enough money to buy it?
5. If the interest rate is 5%, what is the present value of a security that pays you $1, 050 next year and $1, 102.50 two years from now? If this security sold for $2200, is the yield to maturity greater or less than 5%? Why?