Can you please explain/redo these as I am unable to understand the following reasonings shown? Thanks :)

Suppose that you have just celebrated your 18th birthday today and have current savings of $9,000 in a bank. You plan to get married when you turn 28. You estimate that the family commitments would imply monthly expenses of $6,000 per month, assumed to be occurring at the beginning of each month for the entire 12-year period after the marriage, after which you hope that you would have achieved financial freedom. From now until age 28, you intend to deposit either equal annual savings, or equal quarterly savings, both of which are made in arrears (i.e., at the end of each period) into the same bank account. The interest rate is 9% per annum compounded annually for the next 10 years and 6% per annum compounded monthly thereafter. (a) Calculate the present value of the future monthly expenses at the time when you turn 28 years old. (2 marks) 0.06 12 0.005 6000 PV10 1 1.005144 x 1.005 0.005 = $617922.70 (b) Calculate the minimum amount of annual savings such that the accumulated balance is sufficient to cover the monthly expenses. (4 marks) PMT 0.09 617922.70 = 9000 1.09 + PMT= $39269.35 (1.090 - 1) (c) By using the answer in part (b) above, calculate the minimum amount of quarterly savings such that the savings goal in part (b) is achieved. (4 marks) i* 1.09-1=0.02178 39269.35 PMT 0.02178 PMT= $9502.36 (1.021784-1) Suppose that you have just celebrated your 18th birthday today and have current savings of $9,000 in a bank. You plan to get married when you turn 28. You estimate that the family commitments would imply monthly expenses of $6,000 per month, assumed to be occurring at the beginning of each month for the entire 12-year period after the marriage, after which you hope that you would have achieved financial freedom. From now until age 28, you intend to deposit either equal annual savings, or equal quarterly savings, both of which are made in arrears (i.e., at the end of each period) into the same bank account. The interest rate is 9% per annum compounded annually for the next 10 years and 6% per annum compounded monthly thereafter. (a) Calculate the present value of the future monthly expenses at the time when you turn 28 years old. (2 marks) 0.06 12 0.005 6000 PV10 1 1.005144 x 1.005 0.005 = $617922.70 (b) Calculate the minimum amount of annual savings such that the accumulated balance is sufficient to cover the monthly expenses. (4 marks) PMT 0.09 617922.70 = 9000 1.09 + PMT= $39269.35 (1.090 - 1) (c) By using the answer in part (b) above, calculate the minimum amount of quarterly savings such that the savings goal in part (b) is achieved. (4 marks) i* 1.09-1=0.02178 39269.35 PMT 0.02178 PMT= $9502.36 (1.021784-1)