Revision as of 21:46, 26 November 2023 by Admin (Created page with "'''Solution: C''' We need <math>t</math> such that <math>(1+i)^t=2</math> so <math>t=\ln 2 /(\ln (1+i))</math>. But <math>4 s_{\overline{2 n} \mid}=9 s_{\bar{n} \mid}</math> so <math>4 \frac{(1+i)^{2 n}-1}{i}=</math> <math>9 \frac{(1+i)^n-1}{i}</math> so <math>4 \frac{\left((1+i)^n-1\right)\left((1+i)^n+1\right)}{i}=9 \frac{(1+i)^n-1}{i}</math> so <math>(1+i)^n+1=9 / 4</math> so <math>(1+i)^n=5 / 4=1.25</math>. Thus <math>n \ln (1+i)=\ln 1.25</math>. Finally <math>t=\ln...")
Exercise
Nov 26'23
Answer
Solution: C
We need [math]t[/math] such that [math](1+i)^t=2[/math] so [math]t=\ln 2 /(\ln (1+i))[/math]. But [math]4 s_{\overline{2 n} \mid}=9 s_{\bar{n} \mid}[/math] so [math]4 \frac{(1+i)^{2 n}-1}{i}=[/math] [math]9 \frac{(1+i)^n-1}{i}[/math] so [math]4 \frac{\left((1+i)^n-1\right)\left((1+i)^n+1\right)}{i}=9 \frac{(1+i)^n-1}{i}[/math] so [math](1+i)^n+1=9 / 4[/math] so [math](1+i)^n=5 / 4=1.25[/math]. Thus [math]n \ln (1+i)=\ln 1.25[/math]. Finally [math]t=\ln 2 /(\ln (1+i))=n \ln 2 / \ln 1.25=3.106 n[/math].
References
Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.