Question $2$: $($Value $4$ marks$)$

Acme Inc. acquired a debt of $$252,000.$ Acme agrees to repay the loan with payments of $$13,500$

made at the end of every three months. Interest is $8\mathrm{.}52\%$ compounded semi$-$annually.

$($a$)$ What is the number of payments needed to retire the debt? $($Give whole number answer$)$

$($b$)$ What is the interest paid in the $12$th payment?

$($c$)$ What is the principal repaid in the ${15}^{th}$ payment?

$($d$)$ What is the cost of the debt $($i$.$e$.$ the interest paid$)$ for the first two years?

Show all inputs and any other necessary work below. Use the table for part $($a$).$

For parts $($b$),($c$),$ and $($d$)$ show the inputs you used for P$1$ and P$2$ in the blank area below.