n investor knows that she will need £20,000 in ten years and looks at possible savings plans. The interest rate is 3% p.a. effective. (a) She pays an annuity due for ten years with each instalment being of amount X. Additionally she makes two lump payments, each one of amount £1,000, at the start of the 1st and 5th year. Find the amount X of each instalment. (b) She pays an annuity immediate payable quarterly for ten years. Find the amount Y of each payment.

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