a$.$ What is an yield curve? If interest rates are expected to rise $($ how the yield curve will behave $($upward sloping, downward sloping, flat$)$ according to the three theories, i$.$e$.,$ Expectations Theory, Liquidity Preference Theory and Market Segmentation Theory. $(5$ points$)$

Suppose that the pure expectations theory holds for the bond rate. Calculate the interest rates in the terms to maturities from one to five years $($interest rates of $1-$year, $2-$year, $3-$ year, $4-$year and $5-$year bonds$)$ from one$-$year interests for the period from the $1$st to the $5$th year. $(5$ points$)$

a$.2\%,3\%,4\%,5\%,6\%$

b$.6\%,5\%,4\%,3\%,2\%$

c$.5\%,5\%,5\%,5\%,5\%$

Plot three yield curves based on a$),$ b$)$and c$).$