Ramli invests RM in an investment bank each year. The dividend % per year that he receives is kept in the bank. Let be the amount accumulated after years including the dividend.

(a) Find the total amount accumulated at the end of the first year including the dividend. (2 marks)

(b) Show that the total amount accumulated at the end of the second year including the dividend is 2 = [(1 + 100) + (1 + 100) 2 ]. (4 marks)

(c) Use parts (a) and (b) to show that the total amount accumulated at the end of the 10th year including the dividend is 10 = (1 + 100 ) [(1 + 100) 10 1]. Hint: Use = ( 1) 1 . (4 marks)

(d) If the dividend paid by the bank is 5% per year, find the amount which must be kept each year so that the accumulated amount at the end of the 10th year is RM50 000. Round up the amount to the nearest ringgit.

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