Actuarial Exam 2/FM Prep: Future Value of Decreasing Annuity-Immediate from Reinvestment

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Financial Math for Actuarial Exam 2 (FM), Video 54. Exercise 2.3.13S of "Mathematics of Investment and Credit", Samuel A. Broverman, 6th Edition.

Exercise #2.3.13S: 1000 is deposited into Fund X, which earns an effective annual rate of 6%. At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y , which earns an effective annual rate of 9%. Determine the accumulated value of Fund Y at the end of year 10.

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why do we have to divide 160 into 100 and 60, and 154 into 100 and 54...etc instead of using decreasing annuity formula for those values?

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