Independent solution

How to solve this Loan Sale Proceeds for a Target Lender Yield question

Setup

Setup

Compute the amount originally advanced from the contractual loan terms.

L=1,000a16‾∣0.07L=1{,}000a_{\overline{16}|0.07}

Model

Model

Under the lender's realized 6% yield, value the first eight receipts and sale proceeds at time zero.

L=1,000a8‾∣0.06+Kv0.068L=1{,}000a_{\overline8|0.06}+Kv_{0.06}^8

Compute

Compute

Rearrange and move the residual value to time 8.

K=1,000(a16‾∣0.07−a8‾∣0.06)(1.06)8=5,159.0548K=1{,}000\left(a_{\overline{16}|0.07}-a_{\overline8|0.06}\right)(1.06)^8=5{,}159.0548

Answer

Answer

The sale price is approximately 5159, choice A.

K≈5,159(A)\boxed{K\approx5{,}159\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 16 · N; 7 · I/Y; 1000 · +/− · PMT; 0 · FV; CPT · PV9,446.65This is the original loan amount.
  2. 8 · N; 6 · I/Y; 9446.65 · +/− · PV; 1000 · PMT; CPT · FV5,159.05The future value is the required time-8 sale receipt.