Jennifer deposits 1000 into an account. Interest is credited at a nominal annual rate of i convertible seminannually for the first 7 years and at rate 2i convertible quarterly for the all years thereafter. The accumulated amount after 5 years is X. The accumulated amount at the end of 10.5 years is 1980.

Calculate X.

• 1200
• 1225
• 1250
• 1275
• 1300

References

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

Solution: D

[[math]] \begin{aligned} & 1000(1+i / 2)^{10}=X .(1) \\ & 1980=1000(1+i / 2)^{14}(1+i / 2)^{14}=1000(1+i / 2)^{28}(2) \\ & \text { From }(2), 1.98=(1+i / 2)^{28} \text { so }(1+i / 2)^{10}=1.98^{10 / 28} \\ & \text { Thus } X=1000(1+i / 2)^{10}=1000 * 1.98^{10 / 28}=1276.30\end{aligned} [[/math]]

References

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