Parents of a new born baby are planning to establish a scholarship fund for their baby. They plan to deposit a lump sum amount of money in an account on the day she is born so that she would be able to withdraw $$24,000$ per year from her $18$ th to her $23$ rd birthdays $($i$.$e$.,6$ annual withdrawals$).$ What should be the lump sum deposit if the fund is expected to earn an interest rate of $6\%$ per year.