A person lent out certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and 2 years is 16:49. The rate of interest per annum is

Options

A. 0.09
B. `8""1/7%`
C. `13""1/3%`
D. None of these

Explanation

To solve the problem, we need to find the rate of interest per annum based on the given ratio of the differences between compound interest (CI) and simple interest (SI) for 3 years and 2 years. Let's break down the solution step by step.

### Step 1: Understand the given information
We are given that the ratio of the difference between compound interest and simple interest for 3 years and 2 years is 16:49.

### Step 2: Formulate the expressions for CI and SI
For a principal amount \( P \) and rate of interest \( r \% \):
- The formula for Simple Interest (SI) for \( n \) years is:
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