Units of RM$1,$ are deposited at the beginning of each year for $n$ years into a

financial instrument offering an interest rate of i annually. The interests are then

re$-$invested into another financial instruments offering the interest rate of $j$

annually.

$($a$)$ Derive the accumulated value of deposited fund at the end of $n$ years

based on i and $j$ above.

$[4$ marks$]$

$($b$)$ At $n=10,i=5\%$ and $j=4\%,$ find $($a$).$

$[3$ marks$]$

$($c$)$ If $j=i,$ show that $($a$)$ is equal to the future value of annuity$-$due at interest

rate of $i.$

$[4$ marks$]$