Independent solution

How to solve this Loan Amortization question

Setup

Setup

Determine the lender's contractual monthly receipt from the loan rate.

R=1000a120‾∣ 0.08/12=12.13276R=\frac{1000}{a_{\overline{120}|\,0.08/12}}=12.13276

Model

Model

Accumulate every received payment at the lender's actual 0.5% monthly reinvestment rate.

F120=Rs120‾∣ 0.06/12=1988.31F_{120}=Rs_{\overline{120}|\,0.06/12}=1988.31

Compute

Compute

Compare the resulting ten-year fund with the original 1,000 advance.

1000(1+j)10=1988.31⟹j=0.07111000(1+j)^{10}=1988.31\Longrightarrow j=0.0711

Answer

Answer

The lender's annual effective yield is approximately 7.1%, corresponding to choice D.

j≈7.1%(D)\boxed{j\approx7.1\%\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 120 N; 8/12 I/Y; 1000 PV; 0 FV; CPT PMTPMT = -12.13276
  2. 120 N; 6/12 I/Y; 0 PV; 12.13276 +/- PMT; CPT FVFV = 1988.31
  3. 10 N; 1000 +/- PV; 0 PMT; 1988.31 FV; CPT I/YI/Y = 7.11