$7.$ Quarterly payments are to be made against a $$47,500$ loan at $5\mathrm{.}95\%$ compounded annually with a six$-$year amortization. $25$ marks $(5$ for each part$)$

a$.$ What is the size of the quarterly payment?

b$.$ Calculate the principal portion of the sixth payment.

c$.$ Calculate the interest portion of the $17$th payment.

d$.$ Calculate how much the principal will be reduced in the fourth year.

e$.$ Calculate the total interest paid in the first year.