(Chapter 2, May.2003.15) John borrows 1000 for 10 years at an annual effective interest rate of 10%. He can repay this loan using the amortization method with payments of P at the end of each year. Instead, John repays the 1000 using a sinking fund that pays an annual effective rate of 14%. The deposits to the sinking fund are equal to P minus the interest on the loan and are made at the end of each year for 10 years.

Determine the balance in the sinking fund immediately after repayment of the loan.

• 213
• 218
• 223
• 230
• 237

References

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

Solution: A

[math]1000=P a_{\overline{10} \mid .10}=P \frac{1-1.1^{-10}}{.10}[/math] so [math]P=\frac{.10(1000)}{1-1.1^{-10}}=162.7454[/math]. Amount in sinking fund after payment of loan is

[[math]] (P-100) s_{\overline{10} \mid .14}-1000=62.7454 \frac{1.14^{10}-1}{.14}-1000=213.3263 . [[/math]]

References

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