T$-$bow's Crossbows $8-$year bonds currently yield $9\mathrm{.}41\%,$ and you are decomposing that rate

into its different premiums. Dr$.$ Knight has estimated that the real, risk$-$free rate is constant at

$2\mathrm{.}25\%,$ and that the maturity risk premium can be defined as $0\mathrm{.}15\%(t-1),$ where $t$ is the

number of years to maturity. You believe the default premium and liquidity premium total

$1\mathrm{.}65\%,$ and are the same for all bonds issued by T$-$bow. Further, the annual inflation rate is

expected to be $4\%,4\%,3\%,$ and $3\%$ for years $5,6,7,$ and $8$ respectively. Determine what the

average annual inflation rate must be over years $1-4.$