1. Consider a Fiat 500 that you can buy for $25,000 in cash. You don’t have any money. However, the dealer also agrees to sell it to you for ten annual payments of $2964, with the first payment due immediately. Show that the annual interest rate would be 4%.
2. Suppose that a different dealer offers to sell you the same Fiat for twenty annual payments of $1834, with the first payment due immediately. Is the annual interest rate higher or lower than 4% (note that you don’t necessarily have to compute the interest rate to answer this question, although you could).
3. You are considering buying the following zero bonds (no coupon payments)
Spanish government bond: F=400, m=2;
Greek government bond: F=200, m=2;
where F=face value and m=maturity.
You hear on the news that the interest rate underlying each of them is i=10%. What must be the price of each bond?
Suppose you want to spend $1,000,000 on bonds. You should find that the price of one bond is higher than that of the other. Does this mean that it is a worse investment for you to spend $1,000,000 on that bond instead of the other one? Why or why not?
4. Suppose now that you do not know the interest rate behind them: indeed, they might have different rates. Moreover, you know that, aside from F, the two bonds are identical in all ways except that one of them is riskier than the other. The price of the Spanish bond is 324, whereas the price of the Greek bond is 128. Which one is the riskier of the two? Briefly explain your reasoning.