Independent solution

How to solve this Equivalent Yield on Irregular Deposits question

Setup

Setup

Accumulate each beginning-of-year deposit through the sequence of credited rates to the common terminal date. Group deposits made under the same rate regime with annuity-due factors.

A=100s¨3‾∣ 0.0816(1.05)4+100s¨2‾∣ 0.1025=659.269A=100\ddot s_{\overline{3}|\,0.0816}(1.05)^4+100\ddot s_{\overline{2}|\,0.1025}=659.269

Model

Model

The actual accumulated value is 659.269. Set this equal to five beginning-of-period deposits under a constant two-year effective rate r₂.

100s¨5‾∣ r2=659.269⟹r2=0.093637100\ddot s_{\overline{5}|\,r_2}=659.269\Longrightarrow r_2=0.093637

Compute

Compute

Solving gives r₂ = 9.3637% per two years. The equivalent annual rate is the square root of 1 + r₂ minus 1, equal to 4.577%, or 4.58%.

i=(1+r2)1/2−1=0.04577i=(1+r_2)^{1/2}-1=0.04577

Answer

Answer

The calculation gives 4.58% for equivalent yield on irregular deposits, matching published choice D.

i=4.58%(D)\boxed{i=4.58\%\quad\text{(D)}}