$10$ and $20$ are deposited into a fund at time $10$ and $15,$ respectively. Interest is credited at discount $d^{(4)}$ for the first $10$ years, and at a interest rate of $i^{(2)}=6\%$ thereafter. $A(30)=100.$ Let $d_4=\frac{d^{(4)}}{4},$ then $($at time $0)$

$($a$)100$

$()03()\mathrm{.}03$

$($b$)100$

$()\mathrm{.}03)$

$(()\mathrm{.}03$

$($c$)100$

$()\mathrm{.}03()\mathrm{.}03$

$($d$)100$

$()03()03$

$($e$)$ none of these

The present values of the two streams of payments below are equal.

$($i$)100$ at time $0,200$ at time $n,$ and $300$ at time $2n.$

$($ii$)500$ at time $10.$

Given that

$()n,$ then an equation of values is

$($a$)500(1+i{)}^{10}=0\mathrm{.}5[100+200(0\mathrm{.}5)+300({0\mathrm{.}5}^2)]$

$($b$)500$

$()10$

$($c$)500$

$()10$

$($d$)500(1+i{)}^{10}=100+\frac{200}{0\mathrm{.}5}+\frac{300}{{0\mathrm{.}5}^2}$

$($e$)$ none of these

The price of a n$-$day T$-$Bill with face value $F$ corresponding to a quoted annual discount rate of $d$ is $($Hint: the fraction of year is $t=$ days $\frac{?}{360},$ when calculating the price. $)$

$($a$)P=F(1-dn)$

$($b$)P=F(1-d\frac{n}{360})$

$($c$)P=F(1+dn)$

$($d$)P=F(1+d\frac{n}{360})$

none of these

Smith buys a $182-$day US T$-$Bill with face value F and sells it $91$ days later at prices which corresponds to a quoted annual discount rate of $d.($Use the result from $(13)$ to find Smith's buying and selling prices and then$)$ find his real rate of return $j($for the $91$ days$).$ Let $t_2=\frac{182}{360}$ and $t_1=\frac{91}{360}.$ Then

$($a$)1+j=\frac{1-d{t}_1}{1-d{t}_2}$

$($b$)1+j=\frac{1-d{t}_2}{1-d{t}_1}$

$($c$)1+j=\frac{1+d{t}_1}{1+d{t}_2}$

$($d$)1+j=\frac{1+t_2}{1+d{t}_1}$

$($e$)$ none of these