A sum was invested under compound interest, interest being...

A sum was invested under compound interest, interest being compounded annually. It fetches $? 14400$ as interest in the second year and $? 17280$ as interest in the third year. Find the annual rate of interest.
(A) $10 \%$
(B) $15 \%$
(C) $20 \%$
(D) $25 \%$

Key Concepts

Rate Determination Through Successive Period Interest Ratios

When the interest earned over consecutive periods is known, the annual rate of interest can be deduced by examining the ratio of these amounts. Since compound interest results in a consistent multiplication factor for each period, this ratio directly corresponds to the factor (1 + rate), allowing the calculation of the annual interest rate.

Interest Earned in a Specific Year

Determining the interest earned in a specific year under compound interest involves calculating the additional amount by which the compounded sum increases during that year. This is done by subtracting the previous year's total from the current year's total, thereby isolating the interest earned during that period.

Compound Interest

Compound interest refers to the process of earning interest on both the initial principal and the accumulated interest from prior periods. This method leads to exponential growth of the investment over time because past interest earnings become part of the principal for calculating future interest.

Annual Compounding

Annual compounding is the practice of calculating and adding interest to the principal once per year. Each year, the interest is computed based on the sum of the original principal and the previously accumulated interest, which then becomes the new base for calculating the next period's interest.

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