Please show in excel, include formulas. Suppose the spot rates of interest for investment horizons of $1$ to $5$ years are

$4\%,$ and for $6$ to $10$ years are $5\%.$

$($a$)$ Compute the forward rates of interest $i_t^F$ for $t=1,2,$cdots,$10.$

$($b$)$ Calculate the present value of an annuity$-$immediate of $$100$ over $10$

years.

$($c$)$ Compute the future value of the annuity$-$immediate at the end of year

$10,$ assuming future payments earn the forward rates of interest, using

equation $(3\mathrm{.}18).$

$($d$)$ Repeat part $($c$)$ using equation $(3\mathrm{.}14).$ You should get the same answer

as in part $($c$).$