An annuity pays $X at the end of each quarter for $12$ years. Suppose the monthly

rate for the annuity is j$.$ A perpetuity pays $Y at the beginning of each half year. Suppose the

quarterly rate for the perpetuity is k$.$ The present value of the perpetuity is three times larger than

the present value of the annuity. Find a expression for Y in terms of X and actuarial

symbols evaluated at the rates j and k