You plan to start regular savings for retirement. You have been offered 3 different savings plans by a financial institution.

• Option 1: You will deposit $600 at the end of each month for the next 20 years. The nominal interest rate is 12% per annum compounded monthly.

a) Calculate the future value of your savings immediately after the last deposit. (1 mark)

b) To help you, your parents will deposit a bonus of $1100 into your savings account at the end of every 5 years, in additional to your deposits in part a). Calculate the future value of your savings immediately after the last deposit. (2 marks)

• Option 2: This savings plan requires you to make your first deposit immediately. You will make regular quarterly deposits for the next 20 years. Your savings goal for retirement is $500,000 (at the end of the 20 years). The effective annual rate is 12%.

c) Calculate the effective quarterly interest rate. (1 mark)

d) Calculate the size of the required quarterly deposit. (2 marks)

• Option 3: You will make regular deposits for the next 20 years. Specifically, you will make regular semi-annual deposits of $6,000 for the next 15 years. Then you will stop saving for a year. After that, you will make regular deposits of $10,000 every 2 years for the remaining 4 years. The first deposit is made 6 months from now. The effective annual rate for the first 16 years (starting today) is 10% and the nominal interest rate in subsequent years is 6% per annum compounded daily.

e) Calculate the future value of your savings immediately after the last deposit. (3 marks)

f) How many deposits it will take for the balance to first exceed $130,000? (1 mark)