An annuity paying $$1,400$ at the end of each month $($except for a smaller final payment$)$ was purchased with $$225,000$ that had accumulated in an RRSP$.$ The annuity provides a semiannually compounded rate of return of $5\mathrm{.}2\%.($Round your answers to $2$ decimal places.$)$

a$.$ What amount of principal will be included in Payment $137?$

Principal $

b$.$ What will be the interest portion of Payment $204?$

Interest $

c$.$ How much will the principal be reduced by Payments $145$ to $156$ inclusive?

Principal paid $

d$.$ How much interest will be paid in the twentieth year?

Interest paid $

e$.$ What will be the final payment?

Final payment $