Question

# Interest rates on 3-year Treasury securities are currently 1.92%, while 10-year Treasury securities yield 5.62%. If...

Interest rates on 3-year Treasury securities are currently 1.92%, while 10-year Treasury securities yield 5.62%. If the pure expectations theory is correct, what does the market believe that 7-year Treasury securities will be yielding 3 years from now? a. 4.03 percent b. 3.70 percent c. 7.21 percent d. 6.04 percent e. 7.58 percent

Given 3 year Treasury rate of interest = 1.92%

10 year Treasury security rate of interest = 5.62% p.a

Let the 7 year Treasury rate of interest be x

As per the Expectation theory

( 1+1.92%)^3 ( 1+x%)^7 = ( 1+5.62%)^10

(1.0192)^3 (1+x%)^7 = (1.0562)^10

1.058713 ( 1+x%)^7 = 1.727673

( 1+x%)^7 = 1.727673/1.058713

( 1+x%)^7= 1.6319

1+x% = 1.6319^1/7

1+x% = 1.6319^ 0.1429

1+x% = 1.0724

x% = 1.0724-1

x% = 0.0724

x% = 7.24%

Hence the 7 year Treasury rate is 7.24%.So the answer is close to 7.21%

So option c) 7.21% is the Correct answer.

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