Independent solution

How to solve this Loan Amortization question

Setup

Setup

Convert the nominal annual rate to 4% per quarter and separate the first payment into interest and principal.

P1=1000−0.04(10000)=600P_1=1000-0.04(10000)=600

Model

Model

Under level payments, successive principal portions grow by one plus the periodic interest rate.

P10=P1(1.04)9=854.0P_{10}=P_1(1.04)^9=854.0

Compute

Compute

The tenth principal portion is about 854, leaving about 146 of the 1,000 payment as interest.

I10=1000−P10=146.0I_{10}=1000-P_{10}=146.0

Answer

Answer

The interest in payment ten is 146, corresponding to choice B.

I10≈146(B)\boxed{I_{10}\approx146\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 4 I/Y; 10000 PV; 1000 +/- PMT; 0 FV; CPT N; 2nd PV; 10 ENTER; ↓; 10 ENTER; ↓; ↓; ↓N = 13.02; INT = -146.01; PRN = -853.99END mode; I/Y is the quarterly effective rate. The AMORT row for payment 10 reproduces its interest portion.