Jack has just started his first job and is planning to save $$1000$ a year for the first $6$ years. He already has $$6,000$ in his account. The rate is $3\%.$

Then he plans to secure a good career for the next $30$ years and will save more during this $$prime$-$time$.$ The rate projected during this time is $5\%.$

After that he will retire and will need $$50,000$ a year for $40$ more years of retirement. The rate is expected to be $4\%.$

How much should Jack save during his $$prime$-$time$$to meet his retirement target?