Independent solution

How to solve this Interest Forgone after Loan Forgiveness question

Setup

Setup

Use a quarterly rate of 1.5% and solve the twenty-payment loan.

10,000=Pa20‾∣0.01510{,}000=Pa_{\overline{20}|0.015}
P=582.4574P=582.4574

Model

Model

Immediately after payment 4, sixteen payments remain.

B4=Pa16‾∣0.015=8,230.8587B_4=Pa_{\overline{16}|0.015}=8{,}230.8587

Compute

Compute

The unpaid scheduled payments contain both remaining principal and future interest.

Iforgone=16P−B4I_{\mathrm{forgone}}=16P-B_4

Answer

Answer

The future interest forgone is approximately 1088, choice C.

Iforgone=9,319.3177−8,230.8587=1,088.4590I_{\mathrm{forgone}}=9{,}319.3177-8{,}230.8587=1{,}088.4590
1,088(C)\boxed{1{,}088\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 20 · N; 1.5 · I/Y; 10000 · PV; 0 · FV; CPT · PMT−582.46Quarterly payment magnitude.
  2. 2nd · AMORT; P1 = 1 · ENTER; ↓; P2 = 4 · ENTER; ↓; ↓BAL = −8,230.86Outstanding balance immediately after payment 4.