Independent solution

How to solve this Total Interest Across Loan Structures question

Setup

Setup

Compute interest separately for the three repayment designs so that simple interest, compound accumulation, and amortization are not mixed.

IS=5000(1.0610−1)=3954.24,IJ=5000(0.06)(10)=3000I_S=5000(1.06^{10}-1)=3954.24,\quad I_J=5000(0.06)(10)=3000

Model

Model

The savings-type balance produces compound interest of 3,954.24; the simple-interest loan produces 3,000; and the level-payment loan has payment 679.35, hence total interest 1,793.40.

P=5000/a10‾∣ 0.06=679.35,IL=10P−5000=1793.40P=5000/a_{\overline{10}|\,0.06}=679.35,\quad I_L=10P-5000=1793.40

Compute

Compute

Adding the three interest amounts gives 8,747.64, which rounds to 8,748.

IS+IJ+IL=8747.64I_S+I_J+I_L=8747.64

Answer

Answer

The calculation gives 8748 for total interest across loan structures, matching published choice D.

I=8748(D)\boxed{I=8748\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 10 N; 6 I/Y; 5000 +/- PV; 0 FV; CPT PMT679.35Use the result to compute ten payments less principal.