Independent solution

How to solve this Loan Amortization question

Setup

Setup

Solve the hypothetical level-payment term to locate the final partial payment.

3400=240an‾∣ 0.045⟹n=23.053400=240a_{\overline{n}|\,0.045}\Longrightarrow n=23.05

Model

Model

Because the term is just over 23, retain 23 full year-end payments and place the drop payment at year 24.

3400=240a23‾∣ 0.045+Xv243400=240a_{\overline{23}|\,0.045}+Xv^{24}

Compute

Compute

The present-value residual is 4.53; accumulating it to year 24 gives 13.04.

X=(3400−240a23‾∣ 0.045)(1.045)24=13.04X=(3400-240a_{\overline{23}|\,0.045})(1.045)^{24}=13.04

Answer

Answer

The settlement payment is 13.04, corresponding to choice E.

X=13.04(E)\boxed{X=13.04\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 4.5 I/Y; 3400 PV; 240 +/- PMT; 0 FV; CPT NN = 23.05
  2. 23 N; CPT FVFV residual at year 23; accumulate one additional yearTwenty-three full payments are followed by the year-24 drop payment.