Formulas and Functions

periodic-rate
In some cases, when working with a series of cash ows, or an investment, or a loan, it may be
necessary to know the interest rate each period. This is the periodic-rate.
periodic-rate is specied as a decimal number using the same time frame (for example, monthly,
quarterly, or annually) as other arguments (num-periods or payment).
Assume that you are purchasing a home. The mortgage broker oers you a loan with an initial
balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, xed monthly payments, and
a balance to be renanced at maturity of $100,000. periodic-rate would be 0.005 (annual rate divided
by 12 to match up with the monthly payment). Or assume that you invest your savings in a certicate
of deposit that has a term of 5 years, has a nominal annual interest rate of 4.5%, and interest
compounds quarterly. periodic-rate would be 0.0125 (annual rate divided by 4 to match the quarterly
compounding periods).
present-value
A present value is a cash ow received or paid at the beginning of the investment or loan period.
present-value is specied as a number, usually formatted as currency. Since present-value is a cash
ow, amounts received are specied as positive numbers and amounts paid are specied as negative
numbers.
Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and
then resell. The initial cash purchase payment (which might consist of a down payment and closing
costs) could be a present-value and would be negative. The initial principal amount of a loan on the
townhouse could also be a present-value and would be positive.
price
The purchase price is the amount paid to buy a bond or other interest-bearing or discount debt
security. The purchase price does not include accrued interest purchased with the security.
price is specied as a number representing the amount paid per $100 of face value (purchase price /
face value * 100). price must be greater than 0.
Assume that you own a security that has a face value of $1,000,000. If you paid $965,000 when you
purchased the security, excluding accrued interest if any, price would be 96.50 ($965,000 / $1,000,000
* 100).
redemption
Bonds and other interest-bearing and discount debt securities usually have a stated redemption
value. This is the amount that will be received when the debt security matures.
redemption is specied as a number representing the amount that will be received per $100 of face
value (redemption value / face value * 100). Often, redemption is 100, meaning that the security’s
redemption value is equal to its face value. value must be greater than 0.
Assume that you own a security that has a face value of $1,000,000 and for which you will receive
$1,000,000 at maturity. redemption would be 100 ($1,000,000 / $1,000,000 * 100), because the face
value and the redemption value are the same, a common case. Assume further though that the issuer
of this security oers to redeem the security before maturity and has oered $1,025,000 if redeemed
one year early. redemption would be 102.50 ($1,025,000 / $1,000,000 * 100).
346 Chapter 13 Additional Examples and Topics