Independent solution

How to solve this Drop Payment question

Setup

Setup

Convert the 5.5% annual effective discount rate to the corresponding effective interest rate, i = 0.055/(1 − 0.055) = 5.820%.

i=(1−0.055)−1−1=0.05820i=(1-0.055)^{-1}-1=0.05820

Model

Model

Value the twenty-nine full payments as an annuity-immediate and the final drop payment one period later. Their present value must equal the loan balance.

16796809=1200000a29‾∣ i+Xv3016796809=1200000a_{\overline{29}|\,i}+Xv^{30}

Compute

Compute

After subtracting the full-payment annuity value, the residual equation gives X = 959,490, or 959,500.

X=959490X=959490

Answer

Answer

The calculation gives 959,500 for drop payment, matching published choice D.

X=959500(D)\boxed{X=959500\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 29 N; 5.820106 I/Y; 16796809 +/- PV; 1200000 PMT; CPT FV−959490The absolute future value is the final drop payment.