A bank customer borrows X at an annual effective rate of 12.5% and makes level payments at the end of each year for n years.

1. The interest portion of the final payment is 153.86.
2. The total principal repaid as of time (n-1) is 6009.12.
3. The principal repaid in the first payment is Y.

Calculate Y.

• 470
• 480
• 490
• 500
• 510

References

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

Solution: B

Let [math]K[/math] be annual payment. Here [math]v=(1+i)^{-1}=8 / 9[/math]. Then [math]153.60=I_n=K(1-v)=K / 9[/math] so [math]K=153.86(9)[/math]. Next [math]P R_n=K-I_n=9(153.86)-153.86=8(153.86)[/math]. Then [math]X=\sum_{i=1}^n P R_i=P R_n+6009.12=[/math] [math]8(153.86)+6009.12[/math]

Thus [math]Y=K-X i=9(153.86)-[8(153.86)+6009.12(9)](1 / 8)=479.6235[/math].

References

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