## Calculate the profit the bank earn each treasury bond, Mathematics

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Financial institutions often create synthetic instruments out of existing instruments.  In this case an investment bank plans to buy Treasury Bonds with 20-year maturities at their current market price of \$1,000 per bond.  Then the bank will create two instruments. One instrument (like a zero coupon bond) will promise only one maturity payment of \$1,000 in 20 years.  The other instrument will pay only interest at the annual coupon interest rate of the bond, which is 6%.  Both of these synthetic instruments can be sold to investors at prices that imply a yield to maturity of 5% per year.  If the bank buys the Treasury bond and converts it into these two synthetic securities and then sells them, how much profit will the bank earn per each Treasury bond?

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