A portfolio contains an annuity and a perpetuity immediate. Suppose the annuity

offers payment of $$600$ at the end of every half year for $8$ years and the perpetuity offers

payments of $$200$ at the end of every quarter. An investor trades the portfolio for one annuity

due paying $X at the beginning of every year for $15$ years. Assume an interest rate of i is offered

every month. Find an expression for X in terms of annuity symbols evaluated at

the interest rate i