At a nominal interest rate of i convertible semi-annually, an investment of 1000 immediately and 1500 at the end of the first year will accumulate to 2600 at the end of the second year.

Calculate i.

• 2.75%
• 2.77%
• 2.79%
• 2.81%
• 2.83%

References

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

Solution: D

Let [math]j=[/math] semi annual interest. [math]2600=1000(1+j)^4+1500(1+j)^2[/math] This is a quadratic in [math]x=(1+j)^2[/math], which simplifies to [math]10 x^2+15 x-26=0[/math] so

[[math]]x=\frac{-15 \pm \sqrt{15^2-4(10)(-26)}}{2(10)}=1.028342[[/math]]

Thus [math](1+j)^2=1.028342[/math] so [math]j=1.028342^5-1=0.01407199=\frac{i^{(2)}}{2}[/math]. Finally [math]i^{(2)}=2(.01407199)=.02814=2.81 \%[/math].

References

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