discount rate of $10\%$ per year. What happens to the value of your investment if the discount

rate decreases to $5\%?$ What if the discount rate increases to $15\%?$

What is the value today of $$5,100$ per year, at a discount rate of $7\mathrm{.}9\%,$ if the first payment is

received $6$ years from today and the last payment is received $20$ years from today?

Given a discount rate of $4\mathrm{.}6\%$ per year, what is the value at Date $t=7$ of a perpetuity stream

of $$7,300$ payments with the first payment at $t=15?$

A local finance company quotes an interest rate of $18\mathrm{.}4\%$ on one$-$year loans. So$,$ if you

borrow $$20,000,$ the interest for the year will be $$3,600.$ Because you must repay a total of

$$23,680$ in one year, the finance company requires you to pay $$23,\frac{680}{12},$ or $$1,973\mathrm{.}33,$ per

month over the next $12$ months. Is the interest rate on this loan $18\mathrm{.}4\%?$ What rate would

legally have to be quoted? What is the effective interest rate?

Williams Software has $6\mathrm{.}4\%$ coupon bonds on the market with $18$ years to maturity. The

bonds make semiannual payments and currently sell for $106\mathrm{.}32\%$ of par. What is the current

yield on the bonds? The YTM$?$ The effective annual yield?

Bond Prices versus Yields

a$.$ What is the relationship between the price of a bond and its YTM$?$

b$.$ Explain why some bonds sell at a premium over par value while others sell at a discount.

What do you know about the relationship between the coupon rate and the YTM for

premium bonds? What about discount bonds? For bonds selling at par value?

c$.$ What is the relationship between the current yield and the YTM for premium bonds? For

discount bonds? For bonds selling at par value.

You want to have $$2\mathrm{.}5$ million in real dollars in an account when you retire in $40$ years. The

nominal return on your investment is $10\mathrm{.}1\%$ and the inflation rate is $3\mathrm{.}4\%.$ What real amount

must you deposit each year to achieve your goal?

Quinoa Farms just paid a dividend of $$2\mathrm{.}95$ on its stock. The growth rate in dividends is

expected to be a constant $3\mathrm{.}4\%$ per year indefinitely. Investors require a $15\%$ rate of return

for the first three years, a return of $13\%$ for the next three years, and a return of $11\%$

thereafter. What is the current share price?

Synovec Co$.$ is growing quickly. Dividends are expected to grow at a rate of $30\%$ for the

next three years, with a growth rate falling off to a constant $4\%$ thereafter. If the required

return is $10\%,$ and the company just paid a dividend of $$2\mathrm{.}65,$ what is the current share

price?