You have a treasury bond that pays $100$100 one year from today and $1,100$1,100 two years from today.You notice that the yield-to-maturity on a one year-zero coupon treasury bond is 1%1% and the yield-to-maturity on a two year-zero coupon treasury bond is 2%2%. What should the price of your bond be?
Question
You have a treasury bond that pays 100 one year from today and 1,100 two years from today.You notice that the yield-to-maturity on a one year-zero coupon treasury bond is 1%1% and the yield-to-maturity on a two year-zero coupon treasury bond is 2%2%. What should the price of your bond be?
Solution
To calculate the price of the bond, we need to discount the future payments by the yield-to-maturity rates.
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First, we discount the $100 payment one year from today by the 1% yield. This is done by dividing the payment by 1 plus the yield:
99.01
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Next, we discount the $1,100 payment two years from today by the 2% yield. However, since this payment is two years in the future, we need to square the denominator:
1,058.82
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Finally, we add these two amounts together to get the price of the bond:
1,058.82 = $1,157.83
So, the price of the bond should be $1,157.83.
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