An investor paid a price $P$ for a $10-$year annuity$-$immediate with an effective rate i which pays $K$ at the end of each year. He reinvests the payments in an account paying $j$ per year. Find an expression for the ten$-$year growth factor in terms of $j$ and $i.$ Hint: Solve $K$ first.

$($a$)|))/(|))$

$($b$)|))/(|))$

$($c$)|)|)$

$($d$)|)|)$

$($e$)$ none of these

Suppose that a transaction has cash inflow of amounts $A_0,A_1,$dots,$A_n$ and cash outflow of amounts $B_0,B_1,$dots,$B_7$ and times $0,1,$dots,$n,$ respectively. Let $C_k=A_k-B_k$ and $i$ be the cost of capital for the cash inflow and $j$ be the rate of return for the cash outflow and

$()j.$ Determine which of the following is false.

$($a$)$ The MIRR for the transaction can be solved from $B_0(1+j{)}^n+$dots$+B_n=A_0(1+i{)}^n+$dots$+A_n$

$($b$)$ The NPV is $C_0+$dots$+C_n$

$()n$

$($c$)$ The profitability index is $()n()n()n$

$($d$)$ Let $O{B}_t$ be the outstanding balance at time $t.$ The project return rate $j$ is such that $O{B}_0=C_0,O{B}_{t+1}=O{B}_t(1+j)+C_{t+1}$ if if $O{B}_t>0,$ and $O{B}_n=0$

$($e$)$ none of these