Units of $$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 instrument offering the interest rate

of $j$ annually.

a$.$ Derive the accumulated function of deposited fund at the end of $n.$

years based on i and $j$ above.

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

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

interest rate of $i.$