A $25-$year annuity was purchased with $$225,000$ that had accumulated in an RRSP$.$ The annuity provides a semi$-$annually compounded rate of $5\mathrm{.}2\%$ and makes equal month end payment.

a$)$ What amount of principal will be included in Payment $206?$

b$)$ What will be the interest portion of payment $18?$

c$)$ How much will payments $50$ to $100$ inclusive reduce the principal balance?

d$)$ How much interest will be paid in the ${14}^{th}$ year?

e$)$ What will be the final payment?