The problem presented involves calculating the expected one-year interest rate that will be in effect next year, given current yield-to-maturity (YTM) rates for one-year and two-year bonds. This is a typical yield curve problem that can be solved using the geometric average or implied forward rate formula.

We are given:

• YTM for one-year bonds: $y_1 = 2.3\% = 0.023$
• YTM for two-year bonds: $y_2 = 7.0\% = 0.070$

To find the expected one-year rate next year, denoted as $r_2$, we use the following formula based on the relationship between bond yields and implied forward rates:

$(1 + y_2)^2 = (1 + y_1)(1 + r_2)$

Step-by-Step Solution:

1. Substitute the known values into the formula:

$(1 + 0.070)^2 = (1 + 0.023)(1 + r_2)$

2. Simplify both sides:

$(1.070)^2 = (1.023)(1 + r_2)$

$1.1449 = 1.023(1 + r_2)$

3. Divide both sides by 1.023 to solve for $1 + r_2$:

$\frac{1.1449}{1.023} = 1 + r_2$

$1.1193 = 1 + r_2$

4. Subtract 1 from both sides to solve for $r_2$:

$r_2 = 1.1193 - 1 = 0.1193$

Thus, the expected one-year rate in decimal form is 0.1193, or 11.93%.

Do you have any questions, or would you like further clarification?

Here are five related questions to expand on this concept:

1. How does the shape of the yield curve affect expectations about future interest rates?
2. What are forward rates, and how are they derived from the yield curve?
3. How would a different two-year bond yield change the expected one-year rate next year?
4. How do bond prices relate to yield-to-maturity?
5. Can forward rates differ significantly from actual future rates?

Tip: Always remember to express interest rates consistently (either as decimals or percentages) throughout your calculations to avoid confusion.