Independent solution

How to solve this Loan Amortization question

Setup

Setup

The lender's overall yield prices the two promised payments even though the contractual yearly rates differ.

100=X1.10+2X1.102,X=39.0323100=\frac{X}{1.10}+\frac{2X}{1.10^2},\qquad X=39.0323

Model

Model

After finding X, apply the first-year contractual rate and subtract the first payment to obtain the remaining balance.

B1=100(1.08)−X=68.9677B_1=100(1.08)-X=68.9677

Compute

Compute

The second payment must exactly extinguish that balance after one more year of interest.

B1(1+i)=2X,i=78.064568.9677−1=0.131899B_1(1+i)=2X,\qquad i=\frac{78.0645}{68.9677}-1=0.131899

Answer

Answer

The required second-year effective rate rounds to 13.2%, which is choice E.

i≈13.2%(E)\boxed{i\approx13.2\%\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 1 N; 68.9677 +/- PV; 0 PMT; 78.0645 FV; CPT I/YI/Y = 13.1899END mode; I/Y is the effective rate for the second year only.