Independent solution

How to solve this Loan Amortization question

Setup

Setup

Set the two loan present values equal and cancel the common base payment X.

Xan‾∣ 0.01=2.01Xa200‾∣ 0.0201Xa_{\overline{n}|\,0.01}=2.01X a_{\overline{200}|\,0.0201}

Model

Model

The higher monthly accumulation factor equals two successive 1% monthly factors.

1.0201=(1.01)21.0201=(1.01)^2

Compute

Compute

Evaluating the second loan's scaled annuity value matches a 400-payment annuity at 1%.

an‾∣ 0.01=98.13168=a400‾∣ 0.01a_{\overline{n}|\,0.01}=98.13168=a_{\overline{400}|\,0.01}

Answer

Answer

The first borrower therefore makes 400 payments, corresponding to choice E.

n=400(E)\boxed{n=400\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 200 N; 2.01 I/Y; 0 FV; 2.01 +/- PMT; CPT PVPV = 98.13168
  2. 1 I/Y; 1 +/- PMT; 0 FV; 98.13168 PV; CPT NN = 400