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65. Explain why an annuity is an example of a geometric series. (1 mark) 66. a) Calculate the final amount of a 20-year long-term savings plan if a payment of $2000 is made at the end of every year. Interest is 8.5% compounded quarterly. (3 marks) b) What happens to the final value of the long-term savings plan if a payment is made at the beginning of every year instead of at the end of every year? (1 mark) 67. Harold deposits $100 a month into a savings account. His bank informs him that his account has changed from earning interest compounded quarterly to interest compounded weekly. Is this good news for Harold? Justify your answer. (2 marks) 68. Jeremiah has a long-term savings plan. For 10 years, he has been investing $150 a month, earning 4.25% interest compounded monthly. How much more would he have saved if he had chosen to make deposits of $200 a month? (5 marks) 69. Darren is 30 and is debating whether he should start investing $100 a month now for retirement at 60 or if he should wait until he is more established at 40 and invest $200 a month then. If the investment earns approximately 10% p.a. compounded monthly, what would you recommend for saving the largest amount? Provide supporting evidence for your decision. (7 marks)