b$)$ A loan is to be repaid by an increasing annuity. The first payment will be $100$ and the payments will increase by $50$ per annum. Payments will be made annually in arrear for ten years. The repayments are calculated using a rate of interest of $5\%$ per annum effective.

i$)$ Calculate the amount of the loan. $[2$ marks$]$

ii$)$ Calculate:

the interest component of the sixth instalment.