The U.S. recently purchased $1 billion of

Chapter , Problem 3-64

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The U.S. recently purchased $1 billion of 30-yearzero-coupon bonds from a struggling foreign nation.The bonds yield 41/2% per year interest. Thezero-coupon bonds pay no interest during their30-year life. Instead, at the end of 30 years,the U.S. government is to receive back its $1billion together with interest at 41/2% per year. A U.S. senator objected to the purchase, claim-ing that the correct interest rate for bonds likethis is 51/4%. The result, he said, was a multi-million dollar gift to the foreign country withoutthe approval of Congress. Assuming the senatorsmath is correct, how much will the foreign countryhave saved in interest when it repays the bonds at41/2% instead of 51/4% at the end of 30 years?

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