A sum was divided into two equal parts. One part was lent at...

A sum was divided into two equal parts. One part was lent at $20 \%$ p.a. simple interest. The other part was lent at $20 \%$ p.a. compound interest, interest being compounded annually. The difference in the interests fetched by the parts in the second year is $? 400$. Find the difference in the interests fetched by the parts in the fourth year (in ?). (A) 1414 (B) 1442 (C) 1456 (D) 1484

Key Concepts

Interest Difference Analysis

Interest difference analysis involves comparing the amount of interest accrued under different interest calculation methods over time. This is important for understanding how compound interest can lead to significantly higher returns compared to simple interest, especially over longer periods where the effects of compounding become more pronounced.

Annual Compounding

Annual compounding refers to the process where the interest earned over one year is added to the principal, so that in the subsequent year, interest is earned on the new, larger principal. This feature is central to compound interest and distinguishes it from simple interest.

Interest Rate

The interest rate is the percentage at which interest accrues on a given principal over a specific period. It plays a crucial role in both simple and compound interest calculations, determining the growth rate of an investment or loan.

Simple Interest

Simple interest is calculated on the original principal amount only. It is computed using a constant rate over a specific period, meaning the interest accrues linearly without taking the accumulated interest from previous periods into account.

Compound Interest

Compound interest is calculated on the principal amount and also on the interest accumulated from previous periods. This leads to exponential growth as the interest for each period is computed on an increasing base, making compound interest a more powerful tool over longer time spans.

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