$3\mathrm{.}3\mathrm{.}4$ Smith can repay a loan of $250,000$ in one of two ways:

$($i$)30$ annual payments based on amortization at $i=\mathrm{.}12$;

$($ii$)30$ annual interest payments to the lender at rate $i=\mathrm{.}10,$ along with $30$ level annual deposits to a sinking fund earning rate $j.$

Find the value of $j$ to make the schemes equivalent.