The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


Topic Key Ideas, Formulas, and Techniques Examples


Yield to maturity, pp. 265–266 • Yield to maturity is the interest rate equivalent to
the coupons and maturity value.


  • Use a present value spreadsheet and guess-and-
    check to fi nd the rate.


An 8% coupon rate $1000
par value bond with 12 years
to maturity sells for $1105.73.
Find the yield to maturity.
(Example 6.2.5)

Inverse Correlation of Bond
Rates and Prices, p. 267


  • As market rates increase, the prices of bonds
    decrease and vice versa.


Jill is planning to take out
a mortgage to buy a house
soon. She hears that bond
prices are rising. Is this good
news for her? (Example 6.2.7)

To tal Debt Service, p. 269 • A bond issuer needs to both make periodic
interest payment and prepare for payment at
maturity.


  • Calculate the sinking fund payment needed to
    accumulate the maturity value and add it to the
    periodic interest payments.


A city issues bonds with $7
million maturity value and a
4.7% semiannual coupon.
Their sinking fund earns 4%.
How much does the city need
semiannually to service this
debt? (Example 6.2.9)

Cash Settlement of a Futures
Contract, pp. 277–278


  • Calculate the total price for the items based on
    the contract price.

  • Compare this to the spot market price at the
    delivery date.


Luis takes a short position
for 5,000 bushels of October
soybeans at 612.5 cents per
bushel. At the delivery date,
the spot market price per
bushel is 543.0 cents per
bushel. Calculate his profi t.
(Example 6.3.2)

Gain or Loss on a Futures
Contract as a Rate,
pp. 278–279


  • Calculate the profi t/loss from the contract.

  • Use the simple interest formula to calculate the
    rate of return, using the initial margin requirement
    as principal.


Jimmy went long 1,000
barrels of September oil at
$75.09. 52 days later he
closed his position at $68.35.
His initial margin was 5%.
Calculate his rate of return.
(Examples 6.3.3 and 6.3.5)

Cash Settlement of an
Options Contract, p. 281


  • Calculate the total price of the stock at its price
    when the option is exercised.

  • Calculate the total price using the strike price.

  • Find the difference between the two.

  • Subtract the option premium.


You believe that a stock
price is likely to drop, and
so you buy a $60 put option
for 500 shares. The option
premium is $2. How will you
make out if the stock price
drops to (a) $50 and (b) $60.
(Example 6.3.7)

Gain or Loss on an Options
Contract as a Percent, p. 281


  • Calculate the profi t/loss from the contract.

  • Use the simple interest formula using the
    premium as the principal.


Calculate the rate of
return for the options
investment described above.
(Example 6.3.8)

Projecting Rates of Return
Based on Asset Allocation,
p. 294


  • Use a realistic long-term rate of return projection
    for each asset class.

  • Calculate a weighted average of these rates
    based on the percent allocation for each class.


Matt has invested 60% in
equities, 30% in fi xed income
and 10% in cash. What
range of rates of return would
be reasonable for him to
expect over the long term?
(Example 6.4.1)

Chapter 6 Summary 303

(Continued)
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