Deposits are to be made to a fund each January 1 and July 1 for the years 1995 through 2005. The deposit made on each July 1 will be 10.25% greater than the one made on the immediately preceding January 1. The deposit made on each January 1 (except for January 1, 1995) will be the same amount as the deposit made on the immediately preceding July 1. The fund will be credited with interest at a nominal annual rate of 10%, compounded semi-annually. On December 31, 2005, the fund will have a balance of 11000.

Determine the initial deposit to the fund.

• 160
• 165
• 175
• 195
• 200

References

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

Solution: B

[[math]] \begin{gathered} \text { January } \quad \text { July } \\ K(1.05)^{22}+K(1.1025)(1.05)^{21} \\ +K(1.1025)(1.05)^{20}+K(1.1025)^2(1.05)^{19} \\ +\ldots+\ldots \\ +K(1.1025)^9(1.05)^2+K(1.1025)^{10}(1.05)^1 \\ =11 K(1.1025)^{11}+11 K(1.1025)^{11}(1.05) \\ =65.96463 K=11000 \end{gathered} [[/math]]

Thus [math]K=11000 / 65.96463=166.7560[/math].