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Determining Price of Bonds

Finding the price of a 10 year pure discount bond paying $1000 at maturity if the YTM is 5%, 10% and 15%

Also, the same company issued a bond with a par of $1000, time to maturity of 20 years, a coupon rate of 8% with semiannual payments. Please calculate the price of this bond if the YTM is 8%, 10% and 6%.

Lastly, If the same company issued 12 year bonds 2 years ago at a coupon rate of 8.6% and the bonds make semiannual payments, if the bonds currently sell for 97% of par value, what is the YTM?

Solution Preview

Please refer attached file for better clarity of formulas and tables.

Solution:

a) I need help finding the price of a 10 year pure discount bond paying $1000 at maturity if the YTM
is 5%, 10% and 15%

Price of bond will be equal to PV of bond
PV = FV/(1+r)^n
n = number of periods
r=discount rate
FV = Future value

Case 1
FV=$1,000
r =5%
n=10
Put these values in the above formula and get PV,
PV = 1000/(1.05)^10=613.91

Case 2
FV=$1,000
r =10%
n=10
Put these values in the above formula and get PV,
PV = 1000/(1.1)^10= 385.54

Case 2
FV=$1,000
r =15%
n=10
Put these values in the above formula and get PV,
PV = 1000/(1.15)^10=247.18

Also, the same company issued a bond with a par of $1000, time to maturity of 20 years, a
coupon rate of 8% ...

Solution Summary

Solution describes the steps for determining price of pure discount bonds and coupon paying bonds. It also explains how to fing YTM of a bond.

$2.19