Equal deposits of $$4300$ are made at the end of each quarter in an account which earns $7\mathrm{.}5\%$ compounded monthly for $5$ years.

a$.$ State the effective rate for $7\mathrm{.}5\%$ compounded monthly to $2$ decimal places.

b$.$ Using the value you got for part a$,$ state the equivalent nominal rate converted quarterly to $7\mathrm{.}5\%$ compounded monthly to $2$ decimal places.

c$.$ Using the nominal rate from part b$,$ determine the balance of the account at the end of $5$ years.

d$.$ If no more deposits are made, but the money is left in the account accumulating interest for $18$ more years, determine the amount in the account at the end of $23$ years. Hint: Use $7\mathrm{.}5\%$ compounded monthly.