On March 28, 2008, Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor, offered some securities for sale to the public. Under the terms of the contract, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC$24,099 for each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a$100,000 payment 30 years later.

Suppose that when TMCC offered the security for $24,099, the U.S. Treasury had offered an essentially identical security. Do you think it would have had a higher or lower price? Why?

At 7.3 percent interest, how long does it take to double your money? To quadruple it?

On March 28, 2008, Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor, offered some securities for sale to the public. Under the terms of the contract, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC$24,099 for each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a$100,000 payment 30 years later.

TMCC has the right to buy back the securities on the anniversary date at a price established when the securities were issued (this feature is a term of this particular deal). What impact does this feature have on the desirability of this security as an investment?

On March 28, 2008, Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor, offered some securities for sale to the public. Under the terms of the contract, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC$24,099 for each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a$100,000 payment 30 years later.

Why would TMCC be willing to accept such a small amount today ($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future?

Suppose the total cost of a college education will be $320,000 when your child enters college in 18 years. You presently have$67,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education?

Take a look at Example 5.7. Is it deceptive advertising? Is it unethical to advertise a future value like this without a disclaimer?

Solve for the unknown number of years in each of the items:

What happens to a future value if you increase the rate r? Moreover, what happens to a present value?

Calculate the unknown interest rate in each of the following:

Give the Rule of 72.

Give the basic present value equation.

As you increase the length of time involved, what happens to future values? Moreover, what happens to present values?

For each of the following, compute the present value:

$$\begin{array}{|l|r|r|r|} \hline \text{Present Value} & \text{Years} & \text{Interest Rate \\\%} & \text{Future Value} \\ \hline & 13 & 9 & 15,451 \\ \hline & 4 & 7 & 51,557 \\ \hline & 29 & 24 & 886,073 \\ \hline & 40 & 35 & 550,164 \\ \hline \end{array}$$

Generally, what is the present value of $1 to be received in t periods, assuming a discount rate of r per period?