Answer: 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 .
