Frugal Aunt Myrtle wishes to leave a perpetuity in trust to her heirs. She saves $X at the end of each year for 50 years. She wants her funds to generate annual level withdrawals of $Y in perpetuity to her heirs. Exactly 10 years after her last deposit, her heirs receive their first payment of $Y. Suppose the annual effective rate of interest is i% for the first 50 years and j% for all years after that. Find a formula for Y in terms only of X, i, and j and actuarial symbols at the appropriate rates. (That is, do not have any d or n or v in your final answer.)

the answer is Y = (X s_50 at ratei) * (1+j) ^10 * j/(1+j), but i need the work to get there