Explanation

The 2-year implied forward rate in one year's time (denoted as $f_{1,2}$) can be calculated using the relationship between spot rates and forward rates.

Formula:

The relationship between spot rates and forward rates is given by:

$(1 + z_3)^3 = (1 + z_1)^1 \times (1 + f_{1,2})^2$

Where:

• $z_1$ = 1-year spot rate = 1.50% = 0.015
• $z_3$ = 3-year spot rate = 2.25% = 0.0225
• $f_{1,2}$ = 2-year forward rate starting in 1 year

Calculation:

$(1 + 0.0225)^3 = (1 + 0.015)^1 \times (1 + f_{1,2})^2$

$(1.0225)^3 = (1.015) \times (1 + f_{1,2})^2$

$1.0690 = 1.015 \times (1 + f_{1,2})^2$

$(1 + f_{1,2})^2 = \frac{1.0690}{1.015} = 1.0532$

$1 + f_{1,2} = \sqrt{1.0532} = 1.0263$

$f_{1,2} = 0.0263 = 2.63$

Wait, let me recalculate more precisely:

$(1.0225)^3 = 1.0225 \times 1.0225 \times 1.0225 = 1.0689$

$1.0689 / 1.015 = 1.0531$

$\sqrt{1.0531} = 1.0262$

$f_{1,2} = 2.62$

However, let me check if the question is asking for the 2-year forward rate starting in 1 year, which would be the rate for years 1 to 3.

Actually, the 2-year implied forward rate in one year's time means the forward rate for the period from year 1 to year 3.

Using the formula: $(1 + z_3)^3 = (1 + z_1)^1 \times (1 + f_{1,2})^2$

Where $f_{1,2}$ is the annual forward rate for years 1-3.

$(1.0225)^3 = 1.015 \times (1 + f)^2$

$1.0689 = 1.015 \times (1 + f)^2$

$(1 + f)^2 = 1.0689 / 1.015 = 1.0531$

$1 + f = \sqrt{1.0531} = 1.0262$

$f = 0.0262 = 2.62$

This is closest to option B: 2.63%.

Let me verify with an alternative approach:

We can also calculate using: $f_{1,2} = \left[\frac{(1 + z_3)^3}{(1 + z_1)^1}\right]^{1/2} - 1$

$f_{1,2} = \left[\frac{(1.0225)^3}{1.015}\right]^{1/2} - 1$

$f_{1,2} = \left[\frac{1.0689}{1.015}\right]^{1/2} - 1$

$f_{1,2} = [1.0531]^{1/2} - 1$

$f_{1,2} = 1.0262 - 1 = 0.0262 = 2.62$

Given the options, 2.63% is the closest.

Therefore, the correct answer is B: 2.63%.