The accumulation function is given by: $a(t)=\sqrt[\phantom{2}]{1+t}$

What is the force of interest ${}_t$ at time $t=1?$

The accumulated value of one at time $t($where $0t1)$ is given by

second degree polynomial in $t.$ You are given:

$($i$)$ The nominal rate of interest convertible semiannually for the first half

of the year is $5\%$ per annum.

$($ii$)$ The effective rate of interest for the year is $4\%$ per annum.

Calculate ${}_{\frac{3}{4}}$

The accumulated value of one at time $t($where $0t1)$ is given by

second degree polynomial in $t.$ You are given:

$($i$)$ The nominal rate of interest convertible semiannually for the first half

of the year is $5\%$ per annum.

$($ii$)$ The effective rate of interest for the year is $4\%$ per annum.

Calculate ${}_{\frac{3}{4}}$