Revision as of 10:36, 18 November 2023 by Admin (Created page with "'''Solution: D''' The first payment is 2,000, and the second payment of 2,010 is 1.005 times the first payment. Since we are given that the series of quarterly payments is geometric, the payments multiply by 1.005 every quarter. Based on the quarterly interest rate, the equation of value is <math display = "block"> \begin{align*} 100,000=2,0000+2,000(1.005)v+2,000(1.005)^{2}v^{2}+2,000(1.005)^{3}v^{3}+\cdots={\frac{2,0000}{1-1.005v}} \\ 1-1.005v=2,000/100,000 \Rightarr...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: D
The first payment is 2,000, and the second payment of 2,010 is 1.005 times the first payment. Since we are given that the series of quarterly payments is geometric, the payments multiply by 1.005 every quarter. Based on the quarterly interest rate, the equation of value is
[[math]]
\begin{align*}
100,000=2,0000+2,000(1.005)v+2,000(1.005)^{2}v^{2}+2,000(1.005)^{3}v^{3}+\cdots={\frac{2,0000}{1-1.005v}} \\
1-1.005v=2,000/100,000 \Rightarrow v=0.98/1.005.
\end{align*}
[[/math]]
The annual effective rate is [math]v^{-4}-1=\left(0.98\,/1.005\right)^{-4}-1=0.10601=10.69 \%. [/math]
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