This formula can only be applied when the frequency

This formula can only be applied when the frequency of the annuity payments is the same as the
compounding period for the interest rate. For example, if the annuity has quarterly payments the
interest rate must be compounded quarterly (m = 4). As with the earlier formula, the Future Value
is computed at the end of the period in which the last annuity payment occurs.
Thus, the earlier Future Value on an Annuity formula is actually just a special case of this
formula since under annual compounding ( i.e., when m = 1) the rate per period is the same as the
nominal rate.
Future Value of an Annuity Example
Find the Future Value at the end of 3 years of an annuity of $100 per quarter for 3 years if the
interest rate is 8% compounded quarterly.

Bond Valuation
Bonds are long-term debt securities that are issued by corporations and government
entities. Purchasers of bonds receive periodic interest payments, called coupon
payments, until maturity at which time they receive the face value of the bond and the
last coupon payment. Most bonds pay interest semiannually. The Bond
Indenture or Loan Contract specifies the features of the bond issue. The following
terms are used to describe bonds.
Par or Face Value
The par or face value of a bond is the amount of money that is paid to
the bondholders at maturity. For most bonds the amount is $1000. It also
generally represents the amount of money borrowed by the bond issuer.
Coupon Rate
The coupon rate, which is generally fixed, determines the periodic
coupon or interest payments. It is expressed as a percentage of the bond's
face value. It also represents the interest cost of the bond issue to the
issuer.
Coupon Payments
The coupon payments represent the periodic interest payments from the
bond issuer to the bondholder. The annual coupon payment is calculated
be multiplying the coupon rate by the bond's face value. Since most
bonds pay interest semiannually, generally one half of the annual coupon
is paid to the bondholders every six months.
Maturity Date
The maturity date represents the date on which the bond matures, i.e., the
date on which the face value is repaid. The last coupon payment is also
paid on the maturity date.
Original Maturity
The time remaining until the maturity date when the bond was issued.
Remaining Maturity
The time currently remaining until the maturity date.
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Call Date
For bonds which are callable, i.e., bonds which can be redeemed by the
issuer prior to maturity, the call date represents the date at which the
bond can be called.
Call Price
The amount of money the issuer has to pay to call a callable bond. When
a bond first becomes callable, i.e., on the call date, the call price is often
set to equal the face value plus one year's interest.
Required Return
The rate of return that investors currently require on a bond.