Independent solution

How to solve this Loan Amortization question

Setup

Setup

In a level-payment amortization, the interest decline from one month to the next becomes an equal increase in principal repaid.

Pk+1=Pk(1+j)P_{k+1}=P_k(1+j)

Model

Model

Thus successive principal portions grow at the monthly interest factor.

(1+j)12=1.10(1+j)^{12}=1.10

Compute

Compute

Payments six and thirty are 24 months apart, or two annual effective periods, giving growth factor 1.10 squared.

P30=P6(1+j)24=500(1.10)2=605P_{30}=P_6(1+j)^{24}=500(1.10)^2=605

Answer

Answer

The later principal portion is 605, which is choice C.

P30=605(C)\boxed{P_{30}=605\quad\text{(C)}}