Independent solution

How to solve this Multi-Level Deposit Accumulation question

Setup

Setup

Let x = (1 + i)ⁿ. The given doubling condition fixes x = 2, allowing all accumulated-value factors at n, 2n, and 3n to be written as short geometric sums.

98s3n‾∣+98s2n‾∣=800098s_{\overline{3n}|}+98s_{\overline{2n}|}=8000

Model

Model

Substitute x = 2 into the two deposit accumulations and factor out 1/i. The target balance equation then becomes 98(7 + 3)/i = 8,000.

(1+i)n=2⟹7+3i=81.6327(1+i)^n=2\Longrightarrow\frac{7+3}{i}=81.6327

Compute

Compute

Solving gives i = 10/81.6327 = 0.1225. Thus the annual effective rate is 12.25%.

i=10/81.6327=0.1225i=10/81.6327=0.1225

Answer

Answer

The calculation gives 12.25% for multi-level deposit accumulation, matching published choice C.

i=12.25%(C)\boxed{i=12.25\%\quad\text{(C)}}