Symbolic Examples for Annuity Valuation
Explore symbolic examples illustrating annuity valuation at different time periods. Dive into the representations of annuity values at various valuation dates using symbolic expressions. Enhance your understanding of annuities in financial mathematics with these visual examples.
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Presentation Transcript
SOA Exam FM Module 2 Section 1 Symbolic Examples (Part 2)
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 3 8 3 3 8 3 3 3 8 8 8 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 years ? = ?????
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 years ? = ?????
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 years ? = ????? ? = 3 ? 6|?+
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 years ? = ????? ? = 3 ? 6|?+
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? years ? = ????? ? = 3 ? 6|?+
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? ? = ????? years ? = 3 ? 6|?+ 8 ? 5|? ??
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? ? = ????? years 1 ? = 3 ? 6|?+ 8 ? 5|? ?? ??= 1 + ?
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? ? = ????? years ? 3 ? 6|+ 8? 5|
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? ? = ????? years ? 3 ? 6|?+ 8? 5|?
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? ? = ????? years ? 3 ? 6|?+ 8? 5|?
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? ? = ????? years ? 3 ? 6|?+ 8? 5|?
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 8 8 8 8 8 3 3 3 3 3 3 ? = ???? ? = ????? years ? = 3 ? 6|?+ 8? 5|? (1 + ?)
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 3 8 3 3 8 3 3 3 8 8 8 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 3 3 3 3 8 3 3 3 8 8 8 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 5 5 5 5 3 3 3 3 3 3 3 3 3 3 3 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 5 5 5 5 3 3 3 3 3 3 3 3 3 3 3 ? = ???? ? = ????? years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 5 5 5 5 3 3 3 3 3 3 3 3 3 3 3 ? = ???? ? = ????? years ? = 3 ?11|?+ 5 ? 5|? ??
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 5 5 5 5 3 3 3 3 3 3 3 3 3 3 3 ? = ???? ? = ????? years ? = 3 ?11|?+ 5 ? 5|? ?? = 3 ?11|?+ 5? 5|? (1 + ?)
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 3 8 3 3 8 3 3 3 8 8 8 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 8 8 3 3 8 3 3 3 8 8 8 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 5 5 5 5 5 8 8 8 8 8 8 8 8 8 8 8 years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 5 5 5 5 5 8 8 8 8 8 8 8 8 8 8 8 ? = ???? ? = ????? years
Symbolic Examples Example 1: Symbolically represent the value of the annuity shown at the valuation date shown. 5 5 5 5 5 5 8 8 8 8 8 8 8 8 8 8 8 ? = ???? ? = ????? years ? = 8 ?11|? 5 ? 6|?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2? 6|?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2? 6|? ? = 2? 6|? 1 + ?5+
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2? 6|? ? = 2? 6|? 1 + ?5+ 2? 5|?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2? 6|? ? = 2? 6|? 1 + ?5+ 2? 5|?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2 ? 5|?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2 ? 5|? ? = 2 ? 5|? 1 + ?5+
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2 ? 5|? ? = 2 ? 5|? 1 + ?5+ 2? 6|?
Symbolic Examples Example 2: Symbolically represent the value of the annuity shown at the valuation date shown. periodic eir = ? periodic eir = ? 2 2 2 2 2 2 2 2 2 2 2 ? 2 ? 5|? ? = 2 ? 5|? 1 + ?5+ 2? 6|?
