In the Liquidity Premium Theory Model, bonds and their corresponding interest rates have two properties:

Term to maturity

Date issued

Lets use the following notion

i$\_$date$^$term

The superscript captures the term, and the subscript denotes the date the bond is issued. Therefore i$\_2025^10$ would be the interest rate of a $10$ year bond, in $2025.$

Investors do not know what the interest rate will be in the future, but they can make predictions.

Suppose the year is $2023$ and investors believe that one$-$year interest rates will take the following values in the future.

Year $20232024202520262027$

Interest rate of $1$ year bond $5\%4\%5\%6\%7\%$

So investors believe a one year bond issued in $2025$ will pay $5\%$ interest.

For every year of term beyond $1$ year, borrowers pay a liquidity premium of $1\%.$ So$,$ a $3$ year bond will pay $2\%$ more than a $1$ year bond, all things held equal.

Answer the following

What is the interest rate of a $1-$year bond sold in $2023?($This is easy and not a trick question.$)$

What is the interest rate of a $2-$year bond sold in $2023?$ Remember to include the interest rates over time, and the liquidity term.

What is the interest rate of a $3-$year bond sold in $2023?$

What is the interest rate of a $4-$year bond sold in $2023?$

What is the interest rate of a $5-$year bond sold in $2023?$

The yield curve plots the interest rates of bonds today of varying term structure. Plot the yield curve.

Now suppose the yield on a $9$ year bond is $3\%,$ and the yield on a $10$ year bond is $5\%.$ The liquidity premium is $\mathrm{.}1\%$ per year. What are interest rates believed to be for a $1-$year bond $($with no liquidity premium$)10$ years from now? $($Hint$,$ you need to use a weighted average. There are $9$ years where the average interest rate is $3\%.$ Note$($Please draw me the yield curves for every answer as well.