Independent solution

How to solve this Rounded Loan Payments question

Setup

Setup

Convert the quoted 8% effective discount rate to effective interest i = 0.08/0.92. Compute the unrounded five-payment amount, then apply the stated rounding rule to obtain 128,000.

i=0.08/(1−0.08)=0.0869565i=0.08/(1-0.08)=0.0869565

Model

Model

The first four payments are 128,000; the final payment is a drop amount X at time 5. Value both components at origination.

R=500000/a5‾∣ i=127535⟹Rrounded=128000R=500000/a_{\overline{5}|\,i}=127535\Longrightarrow R_{\rm rounded}=128000

Compute

Compute

Solving 500,000 = 128,000a-angle-4 + Xv⁵ gives X = 125,227, which rounds to 125,200.

500000=128000a4‾∣ i+Xv5⟹X=125227500000=128000a_{\overline{4}|\,i}+Xv^5\Longrightarrow X=125227

Answer

Answer

The calculation gives 125,200 for rounded loan payments, matching published choice D.

X=125200(D)\boxed{X=125200\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 4 N; 8.695652 I/Y; 500000 +/- PV; 128000 PMT; CPT FV−125227The absolute future value at time 4 is carried one more period by the TVM convention used in the equation.