Difference between Compound Interest and Simple Interest

To find the sum of money, we first need to understand the difference between compound interest and simple interest.

Simple Interest:
- Simple interest is calculated based on the principal amount and the interest rate for a specific period of time.
- The formula to calculate simple interest is:
Simple Interest = (Principal * Rate * Time) / 100

Compound Interest:
- Compound interest is calculated based on the principal amount, the interest rate, and the frequency of compounding over a specific period of time.
- The formula to calculate compound interest is:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal

Given Information:
- Interest rate: 6 2/3% per annum
- Time: 3 years
- Difference between compound interest and simple interest: Rupees 46

Calculating the Difference:
Let's assume the principal amount as 'P'.

Simple Interest:
Using the formula for simple interest, we can calculate the simple interest for 3 years as:
Simple Interest = (P * 20/3 * 3) / 100 = 20P/100 = P/5

Compound Interest:
Using the formula for compound interest, we can calculate the compound interest for 3 years as:
Compound Interest = P * (1 + 20/100)^3 - P = P * (6/5)^3 - P

Finding the Sum:
The given difference between compound interest and simple interest is 46 rupees. So, we can set up the equation:
P * (6/5)^3 - P - P/5 = 46

Simplifying the equation:
P * (216/125) - 6P/5 = 46
(216P - 150P) / 125 = 46
66P / 125 = 46
P = (46 * 125) / 66
P = 87.5

Therefore, the sum of money is 87.5 rupees.