A loan of X has an effective annual rate 8%. It is to be repaid by the end of 10 years. If the loan is repaid with a single payment at time t = 10, the total interest paid is $468.05 more than if the loan were repaid by ten equal annual payments. Find the value of X.

• 700
• 710
• 720
• 740
• 760

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} & \text { Total Interest } 1=X(1.08)^{10}-X=X\left(1.08^{10}-1\right)=1.158925 X \\ & \text { Total Interest } 2=\frac{X}{a_{\overline{10}}}\left(10-a_{\overline{10 \mid}}\right)=0.4902949 X \\ & 468.05=1.158925 X-0.4902949 X=0.6686301 X \text { so } X=700.01\end{aligned}[/math]

References

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