If it is assumed that $$200,000$ will be needed $10$ years from now for a college fund, how much

must be invested today at $6\%$ nominal annual rate compounded

a$)$ Interest compounded continuously and payments continuous

b$)$ Interest compounded continuously but payments quarterly

c$)$ Interest compounded continuously but payments annually

d$)$ Interest compounded quarterly and payments quarterly

e$)$ Interest compounded semi$-$annually and payments semi$-$annually

f$)$ Interest compounded quarterly and payments monthly