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Financial Planning and Withdrawal Strategy: Mathematical Analysis

Learn a financial strategy where you deposit a certain amount annually, let it grow, then withdraw strategically. Explore the math behind maximizing returns and optimizing withdrawals.

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Financial Planning and Withdrawal Strategy: Mathematical Analysis

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Presentation Transcript

  1. STEP Numbers, sequences and series

  2. STEP 1 sequences/series: illustration 1

  3. STEP 1 sequences/series: illustration 2

  4. STEP 1 sequences/series: illustration 2

  5. STEP 1 sequences/series: illustration 3 My bank pays p% interest at the end of each year. I start with nothing in my account. Then, for m years, I deposit £a in my account at the beginning of each year. After the end of the mth year, I neither deposit nor withdraw for l years. Show that the total amount of in my account at the end of this period is At the beginning of each of the n years following this period I withdraw £b and this leaves my account empty after the nth withdrawal. Find an expression for a/b in terms of r, l, m, and n. v v v v v v v

  6. STEP 1 sequences/series: illustration 3 My bank pays p% interest at the end of each year. I start with nothing in my account. Then, for m years, I deposit £a in my account at the beginning of each year. After the end of the mth year, I neither deposit nor withdraw for l years. Show that the total amount of in my account at the end of this period is At the beginning of each of the n years following this period I withdraw £b and this leaves my account empty after the nth withdrawal. Find an expression for a/b in terms of r, l, m, and n. v v

  7. STEP 2 sequences/series: illustration 4

  8. STEP 2 sequences/series: illustration 5

  9. STEP 2 sequences/series: illustration 5

  10. STEP 2 sequences/series: illustration 5

  11. BLANK

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