Today is Kyle's birthday and he decides to start saving for his 2-year long Law degree. He will start the program on his 35th birthday. He will need $30,000 to pay for the tuition and living expenses at the beginning of the first semester (6-month long) of the program. Due to inflation, he is expecting that this cost will increase by 5% in the second semester, and will keep increasing at the same rate in the remaining semesters of his study.
Kyle will make his first deposit into an account paying 1% monthly (and so compounded each month as well) in the amount of $1,127.5 one month from today, and he will continue to make an identical deposit each month up to and including the day he turns 35 and starts his Law degree.
What birthday is Kyle celebrating today? Calculate and explain in words all calculations.