Independent solution

How to solve this Loan Balances and Amortization question

Setup

Setup

Convert the annual effective rate to a quarterly rate and value the loan one quarter before the first payment.

j=(1.06)1/4−1j=(1.06)^{1/4}-1
V5=50000(1+j)5V_5=50000(1+j)^5

Model

Model

At quarter 5, the level quarterly payments form an annuity-immediate.

V5=2125an‾∣jV_5=2125a_{\overline n|j}

Compute

Compute

The exact term is 31.865088, so 31 full payments of 2,125 are made before the final smaller payment.

n=31.86508781n=31.86508781

Answer

Answer

There are 31 payments of 2,125, selecting choice D.

31 full payments(D)\boxed{31\text{ full payments}\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVM · 5 · N · 1.467385 · I/Y · 50000 · +/- · PV · 0 · PMT · CPT · FVFV = 53777.71
  2. 53777.71 · +/- · PV · 2125 · PMT · 0 · FV · CPT · NN = 31.87Take the integer number of full payments before the drop.