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$.$