Independent solution

How to solve this Interest Portion Progression question

Setup

Setup

Express the relevant interest portions of a level-payment loan using powers of v. The two supplied ratios first determine v and then the remaining term n.

1−v2=0.525(1−v4)⟹v=0.951191-v^2=0.525(1-v^4)\Longrightarrow v=0.95119

Model

Model

The first relation reduces to v = 0.95119. Substitution into the second gives vⁿ = 0.332596.

1−v2=0.1427(1−vn)1-v^2=0.1427(1-v^n)

Compute

Compute

Taking logarithms yields n = 22 payment periods.

n=ln⁡(0.332596)/ln⁡(0.95119)=22n=\ln(0.332596)/\ln(0.95119)=22

Answer

Answer

The calculation gives 22 for interest portion progression, matching published choice C.

n=22(C)\boxed{n=22\quad\text{(C)}}