The difference between the compound interest and simple interest on a certain sum at 5 % for 2 y

Step 1: Let the principal amount (the sum) be denoted as ( P ). Step 2: Calculate the simple

The difference between the compound interest and simple...

Key Concepts

Simple Interest

Simple interest is calculated using the formula SI = P × r × t, where P is the principal amount, r is the annual rate of interest in decimal form, and t is the time in years. This method computes interest solely on the original principal, without accounting for any interest on previously earned interest.

Compound Interest

Compound interest is determined by the formula CI = P × (1 + r)^t - P, where P represents the principal, r is the annual interest rate in decimal form, and t is the time in years. Unlike simple interest, compound interest accumulates on both the initial amount and the interest that has previously been added to it, resulting in a higher accrual over time.

Difference between Compound and Simple Interest

The difference between compound interest and simple interest becomes evident due to the compounding effect where interest is calculated on accumulated interest. Over 2 years, the mathematical difference can be simplified to an expression involving the square of the rate multiplied by the principal (P × r²), which shows how the additional interest accrues after compounding during the second year.

Interest Rate and Time Considerations

The interest rate and the time period are fundamental in determining the amount of interest accrued in both simple and compound calculations. The rate must be converted into a decimal for these calculations, and the length of time affects how much additional interest is compounded, particularly in compound interest scenarios.

The difference between the compound interest and simple interest on a certain sum at $5 \%$ for 2 years is Rs. 1.50. The sum is (a) Rs. 700 (b) Rs. 600 (c) Rs. 500 (d) None of these

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