8. (Extra credits, 5 pts) Kathryn deposits $100 into account at the beginning of each 4-ycar period for 40 years. The account credits interest at an annual effective interest rate of i. The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years. Then what is X? You can solve this problem in following steps. a. What is the present value in formula)? b. Using your answer in part a, what is the accumulated value at end of 40 years, or X. And what is the accumulated value at end of 20 years, say Y? c. Let X=57. Solve for (1+i). Hint: (1-1)) = (1-6)) (1+ (13-))
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