# Question please asnwer correctly , please . ive spent so much money but i get wrong answers . please help . ❤️ Question 2 (20 marks) a) Carter expects to live for 30 years more after his retirement. He would like to withdraw $$\ 120,000$$ every year from his investment account (Account A) to pay for his living expenses. Carter's investment account (Account A) pays $$5 \%$$ interest per year. How much money (a lump-sum) will Carter required to deposit in Account A at the beginning of his retirement (at age 60 ) to pay for his living expenses if (i) Account $$\mathrm{A}$$ start to pay interest one year after his retirement? ( 5 marks) (ii) Account A start to pay interest on the day of his retirement? ( 5 marks) [Hint: The total deposit that Carter made at the beginning of his retirement in Account A should be the same as the amount required to provide for the monthly living expenses during his retirement years.] b) Continued with part (aii). Suppose Carter has just had his $$35^{\text {th }}$$ birthday today and decided to begin his retirement (exactly) 25 years from now, at his age of 60 . To ensure having sufficient funds to meet his goal, Carter plans to start depositing a fixed amount at the end of every month to a retirement savings account (Account B) that pays an interest of $$12 \%$$, compounded monthly. The first deposit will be made today (on his $$35^{\text {th }}$$ birthday) and the last on his $$58^{\text {m }}$$ birthday. (i) Compute the size of the monthly deposit into Account B that will allow Carter to meet the financial goal of his retirement. ( 8 marks) (ii) If Carter is going to make one single (lump-sum) deposit into Account $$\mathrm{B}$$ on his $$40^{\text {th }}$$ birthday instead, how much will that be for him to achieve the goal? (2 marks)

Transcribed Image Text: Question 2 (20 marks) a) Carter expects to live for 30 years more after his retirement. He would like to withdraw $$\ 120,000$$ every year from his investment account (Account A) to pay for his living expenses. Carter's investment account (Account A) pays $$5 \%$$ interest per year. How much money (a lump-sum) will Carter required to deposit in Account A at the beginning of his retirement (at age 60 ) to pay for his living expenses if (i) Account $$\mathrm{A}$$ start to pay interest one year after his retirement? ( 5 marks) (ii) Account A start to pay interest on the day of his retirement? ( 5 marks) [Hint: The total deposit that Carter made at the beginning of his retirement in Account A should be the same as the amount required to provide for the monthly living expenses during his retirement years.] b) Continued with part (aii). Suppose Carter has just had his $$35^{\text {th }}$$ birthday today and decided to begin his retirement (exactly) 25 years from now, at his age of 60 . To ensure having sufficient funds to meet his goal, Carter plans to start depositing a fixed amount at the end of every month to a retirement savings account (Account B) that pays an interest of $$12 \%$$, compounded monthly. The first deposit will be made today (on his $$35^{\text {th }}$$ birthday) and the last on his $$58^{\text {m }}$$ birthday. (i) Compute the size of the monthly deposit into Account B that will allow Carter to meet the financial goal of his retirement. ( 8 marks) (ii) If Carter is going to make one single (lump-sum) deposit into Account $$\mathrm{B}$$ on his $$40^{\text {th }}$$ birthday instead, how much will that be for him to achieve the goal? (2 marks)
Transcribed Image Text: Question 2 (20 marks) a) Carter expects to live for 30 years more after his retirement. He would like to withdraw $$\ 120,000$$ every year from his investment account (Account A) to pay for his living expenses. Carter's investment account (Account A) pays $$5 \%$$ interest per year. How much money (a lump-sum) will Carter required to deposit in Account A at the beginning of his retirement (at age 60 ) to pay for his living expenses if (i) Account $$\mathrm{A}$$ start to pay interest one year after his retirement? ( 5 marks) (ii) Account A start to pay interest on the day of his retirement? ( 5 marks) [Hint: The total deposit that Carter made at the beginning of his retirement in Account A should be the same as the amount required to provide for the monthly living expenses during his retirement years.] b) Continued with part (aii). Suppose Carter has just had his $$35^{\text {th }}$$ birthday today and decided to begin his retirement (exactly) 25 years from now, at his age of 60 . To ensure having sufficient funds to meet his goal, Carter plans to start depositing a fixed amount at the end of every month to a retirement savings account (Account B) that pays an interest of $$12 \%$$, compounded monthly. The first deposit will be made today (on his $$35^{\text {th }}$$ birthday) and the last on his $$58^{\text {m }}$$ birthday. (i) Compute the size of the monthly deposit into Account B that will allow Carter to meet the financial goal of his retirement. ( 8 marks) (ii) If Carter is going to make one single (lump-sum) deposit into Account $$\mathrm{B}$$ on his $$40^{\text {th }}$$ birthday instead, how much will that be for him to achieve the goal? (2 marks)
&#12304;General guidance&#12305;The answer provided below has been developed in a clear step by step manner.Step1/2a)(i) If Account A starts to pay interest one year after his retirement, Carter will need to deposit a lump-sum amount such that it can grow to $120,000*(1/0.05) =$2,400,000 in 29 years (since the interest is not paid in the first year). Using the formula for the future value of a lump sum investment:FV = PV*(1+r)^nwhere FV is the future value, PV is the present value (the lump sum Carter needs to deposit), r is the interest rate, and n is the number of years, we can solve for PV:PV = FV/(1+r)^n = $2,400,000/(1+0.05)^29 =$734,367.89Therefore, Carter will need to deposit $734,367.89 in Account A at the beginning of his retirement to be able to withdraw$120,000 every year for 30 years.(ii) If Account A starts to pay interest on the day of his retirement, Carter will need to deposit a lump-sum amount such that it can grow to $120,000*(1/0.05) =$2,400,000 in 30 years. Using the same formula as above:PV = FV/(1+r)^n = $2,400,000/(1+0.05)^30 =$1,047,128.92Explanation:Therefore, Carter will need to deposit \$1,047,128.92 in Account A at the beginning of his retirement to b ... See the full answer