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Finance

 yieldtomaturity
 yield to maturity of a level coupon bond

 Calling Sequence yieldtomaturity(amount, face, couponrate, maturity)

Parameters

 amount - present value of the bond face - face value of the bond couponrate - rate indicated by the bond maturity - number of periods to maturity

Description

 • The function yieldtomaturity the interest rate rate of a bond with face value face, present value amount, maturing in maturity period and paying at a rate couponrate per period.
 • The coupon rate is the rate that determines the payments that the bond gives.
 • This function is closely related to the Finance[levelcoupon] function.
 • Since yieldtomaturity used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[yieldtomaturity]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[yieldtomaturity].

Examples

Compare these examples with those in Finance[levelcoupon] I hold a bond with face value of 1000 units with an annual coupon rate of 12%. The coupon is paid twice yearly. The maturity is in 3 years. What is the yield to maturity of the bond, compounded semi-annually given that its present value is 1050.75 units?

 > $\mathrm{with}\left(\mathrm{Finance}\right):$

There are 6 periods of half a year until maturity.

 > $\mathrm{yieldtomaturity}\left(1050.75,1000,\frac{0.12}{2},6\right)$
 ${0.05000132125}$ (1)

Yield is 5% per half year, therefore it is

 > $\cdot 2$
 ${0.1000026425}$ (2)

10% per year. If the present value is the same as the face value

 > $\mathrm{yieldtomaturity}\left(1000,1000,\frac{0.12}{2},6\right)\cdot 2$
 ${0.1200000000}$ (3)

In other words, the yield is identical to the coupon rate when the bond is valued at par. (Remember that the extra factor of 2 is to convert the semi-annual yield to annual yield).

Now let the present value decline to less than face.

 > $\mathrm{yieldtomaturity}\left(952.33,1000,\frac{0.12}{2},6\right)\cdot 2$
 ${0.1400019931}$ (4)

This example shows that the yield must increase when the value of the bond declines.

Compatibility

 • The Finance[yieldtomaturity] command was introduced in Maple 15.