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a) Calculate the present value of the following annuities: (i) Payments of $100 every six months for 10 years given an interest rate of 6.00% p.a. with semi-annual compounding. There are 20 payments in total and each payment is made at the end of the six month period. (ii) Payments of $500 every three months for 5 years given an interest rate of 5.00% p.a. with quarterly compounding. Each payment is made at the start of the corresponding period.