Independent solution

How to solve this Loan Balances and Amortization question

Setup

Setup

Compute the original monthly payment at 7.5% nominal convertible monthly.

R=60000a180‾∣0.075/12R=\frac{60000}{a_{\overline{180}|0.075/12}}

Model

Model

Use the balance under the old rate to locate the refinance date, then solve the new-rate annuity term.

49893=Ram‾∣0.075/1249893=Ra_{\overline{m}|0.075/12}
49893=Ran‾∣0.06/1249893=Ra_{\overline{n}|0.06/12}

Compute

Compute

The old schedule has 132.00 payments remaining, so 48 were made. The new exact term is 119.3239, requiring 120 actual payments including the final smaller one.

Ntotal=48+⌈119.323902⌉=168N_{\mathrm{total}}=48+\lceil119.323902\rceil=168

Answer

Answer

The borrower makes 168 payments in total, so choice D is correct.

N=168(D)\boxed{N=168\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVM · 180 · N · 0.625 · I/Y · 60000 · +/- · PV · 0 · FV · CPT · PMTPMT = 556.21Monthly periods; END mode.
  2. 0.625 · I/Y · 49893 · +/- · PV · 556.21 · PMT · 0 · FV · CPT · NN = 132.00
  3. 0.5 · I/Y · CPT · NN = 119.32Round up because the last payment is smaller.