Alex and Taylor each have a savings account at ABC Bank, which provides the same effective...

  

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Alex and Taylor each have a savings account at ABC Bank, which provides the same effective annual rate (EAR) and allows for various deposit frequencies to suit their individual saving preferences. (a) Alex has decided to contribute $5,000 every quarter, starting today, to a home renovation fund at ABC Bank. He will make these quarterly deposits for a period of 10 years at an annual percentage rate (APR) of 6%, which is compounded quarterly. Calculate the future value of these cash flows at the end of the 10-year period. 0 2 $5000 $5000 $5000 $5000 $5000 $5000 $5000 $5000 $5000 9 10 Year $5000 $5000 $5000 $5000 (5 marks) (b) Under the same savings account conditions, Taylor has decided to make annual deposits of $20,000 for 10 years, with the first deposit occurring one year from today, into a vacation savings account at ABC Bank. Calculate the future value of these cash flows at the end of the 10-year period. 0 9 10 Year $20000 $20000 $20000 $20000 (5 marks) Part II Starting at age 30 (time period = 0), you have set a personal goal to retire at 60 and spend the first ten years of retirement living in Japan. To realize this, you plan to create a savings plan that involves making annual end-of-year deposits, with the amount specified as SC, starting at age 31. You will continue this disciplined saving practice until you are 60, ensuring you build up the necessary funds for retirement. Upon retirement, you aim to make a series of ten annual withdrawals, with the first withdrawal of $80,000 at age 60, to fund your lifestyle in Japan. Throughout the savings period, as well as during your retirement, you are targeting a 12% annual return on your investments. (a) On the timeline provided below, mark the critical time points at the positions indicated by the question marks (?). Label these points with the corresponding cash flows, which include the annual deposits and annual withdrawals at these critical time points respectively. 0 ? ? Year Annual Deposits Annual Withdrawals (4 marks) (b) Calculate the total sum you'll need by age 60 to ensure you can withdraw $80,000 yearly for retirement living in Japan. (4 marks) (c) Calculate the annual deposits you'll make from age 31 till age 60 to ensure you can withdraw $80,000 yearly for retirement living in Japan. (4 marks) Alex and Taylor each have a savings account at ABC Bank, which provides the same effective annual rate (EAR) and allows for various deposit frequencies to suit their individual saving preferences. (a) Alex has decided to contribute $5,000 every quarter, starting today, to a home renovation fund at ABC Bank. He will make these quarterly deposits for a period of 10 years at an annual percentage rate (APR) of 6%, which is compounded quarterly. Calculate the future value of these cash flows at the end of the 10-year period. 0 2 $5000 $5000 $5000 $5000 $5000 $5000 $5000 $5000 $5000 9 10 Year $5000 $5000 $5000 $5000 (5 marks) (b) Under the same savings account conditions, Taylor has decided to make annual deposits of $20,000 for 10 years, with the first deposit occurring one year from today, into a vacation savings account at ABC Bank. Calculate the future value of these cash flows at the end of the 10-year period. 0 9 10 Year $20000 $20000 $20000 $20000 (5 marks) Part II Starting at age 30 (time period = 0), you have set a personal goal to retire at 60 and spend the first ten years of retirement living in Japan. To realize this, you plan to create a savings plan that involves making annual end-of-year deposits, with the amount specified as SC, starting at age 31. You will continue this disciplined saving practice until you are 60, ensuring you build up the necessary funds for retirement. Upon retirement, you aim to make a series of ten annual withdrawals, with the first withdrawal of $80,000 at age 60, to fund your lifestyle in Japan. Throughout the savings period, as well as during your retirement, you are targeting a 12% annual return on your investments. (a) On the timeline provided below, mark the critical time points at the positions indicated by the question marks (?). Label these points with the corresponding cash flows, which include the annual deposits and annual withdrawals at these critical time points respectively. 0 ? ? Year Annual Deposits Annual Withdrawals (4 marks) (b) Calculate the total sum you'll need by age 60 to ensure you can withdraw $80,000 yearly for retirement living in Japan. (4 marks) (c) Calculate the annual deposits you'll make from age 31 till age 60 to ensure you can withdraw $80,000 yearly for retirement living in Japan. (4 marks)