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

7.24%

Explanation:

From the question, we are told that:

3 years treasury securities have an interest rate = 1.92%

10 years treasury security has an interest rate = 5.62%

Let the 7 year treasury security interest in 3 years be represented by z.

Based on the expectation theory

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

(1+0.0192)^3 × (1 + z%)^7 = (1 + 0.0562)^10

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

1.05871(1 + z%)^7 = 1.72767

Divide both side by 1.05871

(1 + z%)^7 = 1.72767/1.05871

(1 + z%)^7= 1.6319

1 + z% = 1.6319^1/7

1 + z% = 1.6319^0.1429

1 + z% = 1.0724

z% = 1.0724 - 1

z% = 0.0724

We then convert the decimal to percentage

z = 7.24%

The market believes that 7-year Treasury securities will be yielding 7.24% in 3 years .