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)

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please asnwer correctly , please . ive spent so much money but i get wrong answers . please help . ❤️

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)
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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)
Community Answer
AEX85B

【General guidance】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