Smith forecasts that interest rates will rise over a $5-$year period

according to a force of interest function given by d$=0\mathrm{.}08+0\mathrm{.}025($t$/$t$+1)$

for $0<=1<=5.$

$($a$)$ According to this scheme, what is the average annual com$-$

pound effective rate for the $5-$year period?

$($b$)$ What are the equivalent annual effective rates for each of

years $1,2,3,4,$ and $5?$

$($c$)$ What is the present value at t $=2$ of $1000$ due at t $=4?$