The risk free rate of interest is $3\mathrm{.}0\%.$ Inflation is expected to be $3\mathrm{.}0\%$ this year, $2\mathrm{.}8\%$ next year $2\mathrm{.}5\%$ the following year and $2\mathrm{.}3\%$ in each of the following years. Assume the liquidity premium is fixed at $1\mathrm{.}25\%$; maturity risk premium is calculated to be $\mathrm{.}1\%(t-1)$; and default risk premium is fixed at $1\mathrm{.}5\%$ for years $1-5$ and $2\mathrm{.}2\%$ for years $6-20.$ Be careful of decimals! Some of the premiums are less than $1\%.$ Calculate the rate for the following:

a$)$ A $5$ year bond.

b$)$ A $15$ year bond.

SHOW WORK IN EXCEL