To save money for a down payment on your first home, you have decided to deposit $$150\mathrm{.}00$ at the end of the month into an account earning interest at $5\mathrm{.}75\%$ compounded quarterly.

a$)$ If you hope to save $$20,000\mathrm{.}00$ for your down payment, determine the number of deposit required to achieve this objected.

b$)$ How long would this take in years?To save money for a down payment on your first home, you have decided to deposit $$150\mathrm{.}00$ at the end of the month into an account earning interest at $5\mathrm{.}75\%$ compounded quarterly.

a$)$ If you hope to save $$20,000\mathrm{.}00$ for your down payment, determine the number of deposit required to achieve this objected.

b$)$ How long would this take in years?