yield to maturity of a level coupon bond - Maple Help

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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?

withFinance:

There are 6 periods of half a year until maturity.

yieldtomaturity1050.75,1000,0.122,6

0.05000132125

(1)

Yield is 5% per half year, therefore it is

2

0.1000026425

(2)

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

yieldtomaturity1000,1000,0.122,62

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.

yieldtomaturity952.33,1000,0.122,62

0.1400019931

(4)

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

See Also

Finance, Finance[levelcoupon], Finance[perpetuity], Finance[presentvalue]


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