A thirty-year annuity X has annual payments of $1,000 at the beginning of each year for twelve years, then annual payments of $2,000 at the beginning of each year for eighteen years. A perpetuity Y has payments of $Q at the end of each year for twenty years, then payments of $3Q at the end of each year thereafter. The present values of X and Y are equal when calculated using an annual effective discount rate of 10%. Find Q.
