The present value of 200 paid at the end of [math]n[/math] years, plus the present value of 100 paid at the end of [math]2 n[/math] years is 200 .

Determine the annual effective rate of interest.

• [[math]]\left(\frac{\sqrt{3}+1}{2}\right)^{1 / n}-1[[/math]]
• [[math]]1-\left(\frac{\sqrt{3}-1}{2}\right)^{1 / n}[[/math]]
• [[math]]\left(\frac{\sqrt{3}-1}{2}\right)^{1 / n}-1[[/math]]
• [[math]]\left(\frac{\sqrt{3}+1}{2}\right)-1[[/math]]
• [[math]]1-\left(\frac{\sqrt{3}-1}{2}\right)^{1/ 2 n}[[/math]]

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Solution: A

[[math]] \begin{aligned} & 200 v^n+100 v^{2 n}=200 \text { so } 0=x^2+2 x-2 \text { so } v^n=x=\frac{-2 \pm \sqrt{4+8}}{2}=-1+\sqrt{3} \text {. But } v=1 /(1+i) \text { so } \\ & i=(1 / v)-1=\left(\frac{1}{\sqrt{3}-1}\right)^{1 / n}-1=\left(\frac{\sqrt{3}+1}{3-1}\right)^{1 / n}-1 \end{aligned} [[/math]]

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.