1. You just turned 24 years old and would like to start saving for your dream car which you plan to buy on your 30th birthday. You have placed $5,000 in a locked-in investment account. a. if you expect the car to cost $90,000 in 6 years what annual rate of return are you required to earn in your locked-in investment account? b. What is the new required annual rate of return you need to earn in your locked-in investment account to be able to afford your dream car? You just turned 30 years old. Your savings and locked-in investment account only have a combined value of $70,000. You decide to take out an auto-loan so you can still purchase your dream car today. The car dealer offers you 2 choices of financing. Choice 1 is a 4 year loan that charges 10% per annum compounded monthly with monthly payments. Choice 2 is a 4 year loan that charges 9.9681% per annum compounded weekly with weekly payments c. What is the monthly payment under choice 1? d. What is the weekly payment under choice 2? e. Show that both choices have approximately the same effective an- nual rate. Is the total interest payments under each plan the same? Explain. 2. You observe three zero-coupon Treasury bonds in the market. Table 1: Treasury Bond Information Maturity 6 months 12 months 18 months Price $970.87 $924.56 $863.81 Treasury bond of 18 months to maturity is about to be issued with a coupon rate of 10% per year (with semi-annual payments). a. Show that the price, per $1,000 face value, of the new bond should be approximately $1,001.80 b. Is the bond selling at a premium or a discount? Why? Without doing any calculations can you say whether or not the yield to maturity will be different than the coupon rate? c. Suppose the coupon bond instead sells at par in the market. Describe how you can exploit this arbitrage opportunity to make money. En- sure that you clearly highlight the cash-flows of your strategy. d. Suppose the expectations theory of term structure holds. What is the market's expectation of the price of the 18-month zero coupon bond 1-year from today (assuming semi-annual compounding)? e. If the liquidity preference theory holds instead, is the expected price of the bond lower or higher than you calculated in part d? Explain.