Independent solution

How to solve this Retrospective Loan Balances question

Setup

Setup

Use a retrospective balance immediately after payment 12: accumulate the original loan and subtract every accumulated payment.

i=0.10i=0.10

Model

Model

The original 12,000 accumulates for 12 years, while the twelve year-end payments accumulate as an annuity-immediate.

B12=12000(1.10)12−1000s12‾∣0.10B_{12}=12000(1.10)^{12}-1000s_{\overline{12}|0.10}

Compute

Compute

The accumulated loan is 37,661.14 and the accumulated payments are 21,384.28.

B12=37661.14−21384.28B_{12}=37661.14-21384.28
B12=16276.86B_{12}=16276.86

Answer

Answer

The balance rounds to 16,277, so the correct answer is D.

B12≈16277(D)\boxed{B_{12}\approx16277\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVMTVM worksheet clearedUse END mode and annual periods.
  2. 12 · NN = 12
  3. 10 · I/YI/Y = 10
  4. 12000 · +/- · PVPV = -12,000
  5. 1000 · PMTPMT = 1,000
  6. CPT · FVFV = 16,276.86