Independent solution

How to solve this Loan Amortization question

Setup

Setup

Calculate the original monthly payment and then value the 192 payments remaining immediately after the June 2009 payment.

P=85000/a240‾∣ 0.005=608.97P=85000/a_{\overline{240}|\,0.005}=608.97

Model

Model

That balance becomes the principal of the refinanced loan at 0.45% per month.

B48=608.97a192‾∣ 0.005=75048.24B_{48}=608.97a_{\overline{192}|\,0.005}=75048.24

Compute

Compute

Solving the new level-payment equation gives 250.62 payment periods, so 250 full payments are followed by a final payment in month 251.

75048.24=500an‾∣ 0.0045⟹n=250.6275048.24=500a_{\overline n|\,0.0045}\Longrightarrow n=250.62

Answer

Answer

Counting 251 months from June 30, 2009 places the last payment on May 31, 2030, choice C.

final payment May 31, 2030(C)\boxed{\text{final payment May 31, 2030}\quad\text{(C)}}

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; 240 N; 0.5 I/Y; 85000 PV; 0 FV; CPT PMTPMT = -608.97END mode; I/Y is the original monthly effective rate.
  2. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 192 N; 0.5 I/Y; 608.97 +/- PMT; 0 FV; CPT PVPV = 75048.24END mode; value the 192 payments remaining immediately after payment 48.
  3. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 0.45 I/Y; 75048.24 PV; 500 +/- PMT; 0 FV; CPT NN = 250.62END mode; I/Y is the refinanced monthly effective rate. A final smaller payment makes the count 251.