Referring to the GMAC security we discussed at the very beginning of the chapter:

a. Based upon the $500 price, what rate was GMAC paying to borrow money?

b. Suppose that, on December 1, 2002, this security’s price was $4,800. If an investor had purchased it for $500 at the offering and sold it on this day, what annual rate of return would she have earned?

c. If an investor had purchased the security at market on December 1, 2002, and held it until it matured, what annual rate of return would she have earned?

Data from GMAC security

On December 2, 1982, General Motors Acceptance Corporation (GMAC), a subsidiary of General Motors, offered some securities for sale to the public. Under the terms of the deal, GMAC promised to repay the owner of one of these securities $10,000 on December 1, 2012, but investors would receive nothing until then. Investors paid GMAC $500 for each of these securities, so they gave up $500 on December 2, 1982, for the promise of a $10,000 payment 30 years later. Such a security, for which you pay some amount today in exchange for a promised lump sum to be received at a future date, is about the simplest possible type.

Is giving up $500 in exchange for $10,000 in 30 years a good deal? On the plus side, you get back $20 for every $1 you put up. That probably sounds good, but, on the down side, you have to wait 30 years to get it. What you need to know is how to analyze this trade-off; this chapter gives you the tools you need.