Independent solution

How to solve this Interest Portion after Refinancing question

Setup

Setup

Convert the original annual effective rate to a monthly rate and solve the 180-payment loan.

j1=1.09121/12−1=0.007299681j_1=1.0912^{1/12}-1=0.007299681
P=100,000a180‾∣j1=1,000.0167P=\frac{100{,}000}{a_{\overline{180}|j_1}}=1{,}000.0167

Model

Model

Immediately after payment 59, 121 original payments remain.

B59=Pa121‾∣j1=80,174.5897B_{59}=Pa_{\overline{121}|j_1}=80{,}174.5897

Compute

Compute

Convert the refinancing rate to its monthly equivalent.

j2=1.05761/12−1=0.004677756j_2=1.0576^{1/12}-1=0.004677756

Answer

Answer

The first refinanced payment's interest portion is balance times monthly rate, about 375, choice A.

I1=B59j2=375.0372I_1=B_{59}j_2=375.0372
I1≈375(A)\boxed{I_1\approx375\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 180 · N; 0.7299681 · I/Y; 100000 · PV; 0 · FV; CPT · PMT−1,000.02Original monthly payment.
  2. 2nd · AMORT; P1 = 1 · ENTER; ↓; P2 = 59 · ENTER; ↓; ↓BAL = −80,174.59Balance immediately after payment 59.