Eric deposits 12 into a fund at time 0 and an additional 12 later into the same fund at time 10. The fund credits interest at an annual effective rate of i. Interest is payable annually and reinvested at an annual effective rate of 0.75i. At time 20, the accumulated amount of the reinvested interest payments is equal to 64.

Calculate i, i > 0.

• 0.092
• 0.096
• 0.10
• 0.104
• 0.11

References

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

Solution: B

[[math]] \begin{aligned} & \begin{array}{llllllll} 0 & 12 i & 12 i & \ldots & 12 i & 24 i & 24 i \ldots 24 i & \text { (Interest Payment) } \end{array} \\ & 1-1-|-\ldots-|-|-| \ldots \mid \\ & \begin{array}{lllllllll} 0 & 1 & 2 & \ldots & 10 & 11 & 12 & \ldots & 20 \end{array} \\ & \text { (Time) } \\ & 64=12 i s_{\overline{20} \mid .75 i}+12 i s_{\overline{10} \mid .75 i}=12 i \frac{(1+.75 i)^{20}-1}{.75 i}+12 i \frac{(1+.75 i)^{10}-1}{.75 i}=16 x^2+16 x-32 \\ & \end{aligned} [[/math]]

where [math]x=(1+.75 i)^{10}[/math]. So [math]16 x^2+16 x-96=0[/math] so [math]x^2+x-6=0[/math] so [math](x+3)(x-2)=0[/math] so [math]x=2[/math]. Then [math](1+.75 i)^{10}=2[/math] so [math]i=.095698[/math]

References

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