Independent solution

How to solve this Loan Reamortization question

Setup

Setup

Determine the original 180-month payment at monthly rate 0.08/12. Immediately after the twelfth payment, value the remaining 168 payments at that original rate to find the balance.

R0=65000/a180‾∣ 0.08/12=621.17R_0=65000/a_{\overline{180}|\,0.08/12}=621.17

Model

Model

Reamortize this balance over the unchanged remaining term using the reduced monthly rate 0.06/12.

B12=R0a168‾∣ 0.08/12=62661.40B_{12}=R_0a_{\overline{168}|\,0.08/12}=62661.40

Compute

Compute

The balance is 62,661.40 and the new payment is 552.19, which rounds to 552.

R1=B12/a168‾∣ 0.06/12=552.19R_1=B_{12}/a_{\overline{168}|\,0.06/12}=552.19

Answer

Answer

The calculation gives 552 for loan reamortization, matching published choice E.

R=552(E)\boxed{R=552\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 180 N; 0.6666667 I/Y; 65000 +/- PV; 0 FV; CPT PMT621.17Original payment.
  2. 168 N; 0.6666667 I/Y; 621.17 PMT; 0 FV; CPT PV−62661.40Balance after payment 12.
  3. 168 N; 0.5 I/Y; 62661.40 +/- PV; 0 FV; CPT PMT552.19Reamortized payment at the new rate.