Independent solution

How to solve this Loan Refinancing question

Setup

Setup

Price the original 40-year level-payment loan at 8%.

20,000=Pa40‾∣0.0820{,}000=Pa_{\overline{40}|0.08}

Model

Model

Immediately after payment 20, value the remaining twenty original payments. Then amortize that balance over the new twenty-year loan.

B20=Pa20‾∣0.08B_{20}=Pa_{\overline{20}|0.08}
B20=Qa20‾∣0.06B_{20}=Qa_{\overline{20}|0.06}

Compute

Compute

The old payment is 1677.2032, the refinance balance is 16467.0285, and the new payment is 1435.6706.

P=1,677.2032P=1{,}677.2032
Q=1,435.6706Q=1{,}435.6706
20P+20Q=62,257.47620P+20Q=62{,}257.476

Answer

Answer

The sum of all forty payments is 62257, choice D.

62,257(D)\boxed{62{,}257\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 40 · N; 8 · I/Y; 20000 · PV; 0 · FV; CPT · PMT−1,677.2032This is the original annual payment.
  2. 20 · N; 8 · I/Y; 1677.2032 · +/− · PMT; 0 · FV; CPT · PV16,467.0285This is the balance immediately after payment 20.
  3. 20 · N; 6 · I/Y; 16467.0285 · PV; 0 · FV; CPT · PMT−1,435.6706This is the replacement annual payment.