Independent solution

How to solve this Loan Amortization question

Setup

Setup

First recover the common monthly payment from the smaller 120-month loan.

30000=Pa120‾∣ 0.0075,P=380.0330000=Pa_{\overline{120}|\,0.0075},\qquad P=380.03

Model

Model

Apply that same payment and monthly rate to the larger advance.

33000=380.03an‾∣ 0.007533000=380.03a_{\overline{n}|\,0.0075}

Compute

Compute

Solving the annuity factor gives a term between 140 and 141 months.

n≈140.5n\approx140.5

Answer

Answer

The loan requires a payment in month 141 to be fully retired, corresponding to choice E.

n=141 months(E)\boxed{n=141\text{ months}\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 120 N; 0.75 I/Y; 30000 PV; 0 FV; CPT PMTPMT = -380.03
  2. 33000 PV; 380.03 +/- PMT; 0 FV; CPT NN ≈ 140.5Round the payment count upward to 141.