Scottie wants to accumulate $$30,000$ for a down payment for a house. He can only afford to set aside $ $300$ at the beginning of every quarter. The account will credit interest annually at the annual rate of $7\mathrm{.}5\%.$ You wish to know how long it will take Scottie to reach his goal. Find c $($the number of interest conversion periods per period interval$)$a$\mathrm{.}3$b$\mathrm{.}1/4$c$\mathrm{.}1$d$\mathrm{.}1/2$e$\mathrm{.}1/6$