Liam wants to be able to buy a house at retirement which is in 15 years. He puts away $X every 6 months starting today for the next 15 years into a savings account that earns a nominal annual rate of 8% compounded quarterly. If the house costs $334000 at the end of 15 years, find the minimum value of X so that Liam can purchase the house outright using the funds in his savings account.

Please show all work and do not use excel, thanks!