Independent solution

How to solve this Loan Refinancing Payment question

Setup

Setup

Find the outstanding balance immediately after payment 18 by accumulating the original loan and subtracting the accumulated value of the first eighteen payments.

B18=22000(1.007)18−450.30s18‾∣ 0.007=16337.10B_{18}=22000(1.007)^{18}-450.30s_{\overline{18}|\,0.007}=16337.10

Model

Model

The retrospective balance is 16,337.10. Treat this as the present value of the refinanced twenty-four-payment loan at 0.4% per month.

B18=Pa24‾∣ 0.004B_{18}=Pa_{\overline{24}|\,0.004}

Compute

Compute

Dividing by the twenty-four-period annuity factor gives the new monthly payment 715.27, or 715.

P=715.27P=715.27

Answer

Answer

The calculation gives 715 for loan refinancing payment, matching published choice D.

P=715(D)\boxed{P=715\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 18 N; 0.7 I/Y; 22000 +/- PV; 450.30 PMT; CPT FV−16337.10The absolute value is the balance after payment 18.
  2. 2nd CLR TVM; 24 N; 0.4 I/Y; 16337.10 +/- PV; 0 FV; CPT PMT715.27Second phase, using the new monthly rate.