Independent solution

How to solve this Interest Rate Valuation question

Setup

Setup

The bonus is based on the initial investment and is added only at the three-year maturity.

AP=1.043+0.02=1.144864A_P=1.04^3+0.02=1.144864

Model

Model

Equate the complete maturity value to the accumulation under a level annual effective rate with no bonus.

(1+i)3=1.144864(1+i)^3=1.144864

Compute

Compute

Taking the cube root gives equivalent annual rate 0.04613.

i=1.1448641/3−1=0.04613i=1.144864^{1/3}-1=0.04613

Answer

Answer

Rounded to one decimal percent, the required rate is 4.6%, choice D.

i=4.6%(D)\boxed{i=4.6\%\quad\text{(D)}}

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; 3 N; 1 +/- PV; 0 PMT; 1.144864 FV; CPT I/YI/Y = 4.6128END mode; I/Y is the equivalent annual effective rate for the three-year maturity factor.