$($a$)$ With reference to part $($a$)$ of Example $3\mathrm{.}7,$ suppose the loan

amount of $100,000$ was not given, but rather that the bor$-$

rower's total annual outlay of $16,902\mathrm{.}95$ was given. Show that

the loan amount is $100,000.$

$($b$)$ A borrower's total annual outlay is $K$ per period for $n$ periods,

including interest at rate $i$ to the lender on a loan of $L,$ and

accumulating the principal in a sinking fund at rate $j$ with $n$

level periodic deposits. Solve for $L$ in terms of $K,n,$i and $j.$