Independent solution

How to solve this Loan Amortization question

Setup

Setup

Ten years of quarterly payments means 40 total payments at 3% per quarter.

10030.27=Rv40−15+1=Rv26,v=1/1.0310030.27=Rv^{40-15+1}=Rv^{26},\qquad v=1/1.03

Model

Model

In a level-payment loan, principal in payment k equals the payment times the discount factor for the number of payments then remaining.

R=10030.27(1.03)26=21631.19R=10030.27(1.03)^{26}=21631.19

Compute

Compute

The known principal portion recovers the level payment, and the remaining-payment formula then gives interest in payment 25.

I25=R(1−v40−25+1)=R(1−v16)=8151.35I_{25}=R(1-v^{40-25+1})=R(1-v^{16})=8151.35

Answer

Answer

The interest component is about 8,151, which is choice B.

I25≈8151(B)\boxed{I_{25}\approx8151\quad\text{(B)}}