A 35 year loan is to be repaid in equal annual installments. The amount of interest paid in the 8th installment is 135. The amount of interest paid in the 22nd installment is 108. Calculate the amount of interest in the 29th installment.

• 72
• 73
• 74
• 75
• 76

References

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

Solution: A

[math]108=K\left(1-v^{14}\right)[/math]

[[math]] 135=K\left(1-v^{28}\right)=K\left(1-v^{14}\right)\left(1+v^{14}\right)=108\left(1+v^{14}\right) \text { so } 1+v^{14}=135 / 108=1.25 \text { so } v^{14}=.25 \text {. } [[/math]]

Thus [math]K=108 /\left(1-v^{14}\right)=108 /(1-.25)=144[/math]. Interest in 29th installment is [math]K\left(1-v^7\right)=144(1-\sqrt{.25})=72[/math].

References

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