Revision as of 20:03, 20 November 2023 by Admin (Created page with "'''Solution: D''' This solution uses time 8 as the valuation time. The two equations to solve are <math display = "block"> \begin{array}{l c r}{{P(i)=300,000(1+i)^{2}+X(1+i)^{8-y}-1,000,000=0}}\\ {{P^{\prime}(i)=600,0000(1+i)+(8-y)X(1+i)^{7-y}=0.}}\end{array} </math> Inserting the interest rate of 4% and solving: <math display = "block"> \begin{align*} 300,000(1.04)^{2}+X(1.04)^{8-y}-1,000,000=0 \\ 600000(1.04)+(8-y)X(1.04)^{7-y}=0 \\ X(1.04)^{-y}=[1.000,000-300,000...")
Exercise
Nov 20'23
Answer
Solution: D
This solution uses time 8 as the valuation time. The two equations to solve are
[[math]]
\begin{array}{l c r}{{P(i)=300,000(1+i)^{2}+X(1+i)^{8-y}-1,000,000=0}}\\ {{P^{\prime}(i)=600,0000(1+i)+(8-y)X(1+i)^{7-y}=0.}}\end{array}
[[/math]]
Inserting the interest rate of 4% and solving:
[[math]]
\begin{align*}
300,000(1.04)^{2}+X(1.04)^{8-y}-1,000,000=0 \\
600000(1.04)+(8-y)X(1.04)^{7-y}=0 \\
X(1.04)^{-y}=[1.000,000-300,000(1.04)^{2}]/1.04^{8}=493,595.85 \\
624,000+(8-y)(1.04)^{7}(493,595.85)=0 \\
y=8+624,000 /\left[493,595.85(1.04)^{7}\right]=8.9607 \\
X=493,595.85(1.04)^{\mathrm{8.9607}}=701,459.
\end{align*}
[[/math]]
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