Revision as of 19:56, 20 November 2023 by Admin (Created page with "'''Solution: D''' <math display = "block"> \begin{array}{l l}{{P_{A}=A(1+i)^{-2}+B(1+i)^{-9}}}\\ {{P_{L}=95,000(1+i)^{-5}}}\\ {{P_{L}^{\prime}=-2A(1+i)^{-9}-9B(1+i)^{-10}}}\end{array} </math> Set the present values and derivatives equal and solve simultaneously. <math display = "block"> \begin{align*} 0.92456A + 0.70259B &= 78, 083 \\ -1.7780.21-6.0801B &=-375,400 \\ B &=\frac{78,083(1.7780/0.92456)-375,400}{0.70259(1.7780/0.92456)-6.0801}=47,630 \\ A &=[78,083-0.7...")
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Exercise

AAdmin
Nov 20'23

Answer

Solution: D

[[math]] \begin{array}{l l}{{P_{A}=A(1+i)^{-2}+B(1+i)^{-9}}}\\ {{P_{L}=95,000(1+i)^{-5}}}\\ {{P_{L}^{\prime}=-2A(1+i)^{-9}-9B(1+i)^{-10}}}\end{array} [[/math]]

Set the present values and derivatives equal and solve simultaneously.

[[math]] \begin{align*} 0.92456A + 0.70259B &= 78, 083 \\ -1.7780.21-6.0801B &=-375,400 \\ B &=\frac{78,083(1.7780/0.92456)-375,400}{0.70259(1.7780/0.92456)-6.0801}=47,630 \\ A &=[78,083-0.70259(47,630)]/0.92456=48,259 \\ \frac{A}{B} &= 1.0132 \end{align*} [[/math]]

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