Eric deposits X into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually. Mike deposits 2X into a different savings account at time 0, which pays simple interest at an annual rate of i. Eric and Mike earn the same amount of interest during the last 6 months of the 8th year.
Calculate i.
References
Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.
Solution: A
[math]X(1+i / 2)^{16}-X(1+i / 2)^{15}=2 X(1+8 i)-2 X(1+7.5 i)[/math] so [math](1+i / 2)^{15} i / 2=2(.5) i[/math] so [math](1+i / 2)^{15}=2[/math] so [math]i / 2=2^{1 / 15}-1=.04729[/math] so [math]i=.09458[/math].
References
Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.