Kris contributes towards a pension for his retirement by depositing into a superannuation fund an amount of $$5000$ on each of his $44$ birthdays from his $21$st to his $64$th inclusive.$($a$)$ If the money is invested at $7\%$ p$.$a$.$ compound interest, how much money is in Kris's superannuation fund on his $65$th birthday Answer:$1423747?($b$)$ As Kris is about to make the deposit on his $43$rd birthday, he is told that he can only expect to earn $3\%$ p$.$a$.$ compound interest for the remainder of the time. How much less will be in the superannuation fund on his $65$th birthday? Answer: $764117$ Please show steps and explain why