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Gitika borrowed a sum of ₹20,000 at a certain rate of simple interest for 2 years. If she paid an interest of ₹4,000 at the end of the period, then find the rate of interest per annum.
10%
20%
15%
25%
10%
Calculate the interest for 1 year: ₹4,000 / 2 = ₹2,000. Now find what percentage ₹2,000 is of ₹20,000: (2000/20000) * 100 = 10%.
Principal (P) = ₹20,000, Time (T) = 2 years, Simple Interest (SI) = ₹4,000
SI=100P×R×T⟹R=P×TSI×100
Calculate the interest for 1 year: ₹4,000 / 2 = ₹2,000. Now find what percentage ₹2,000 is of ₹20,000: (2000/20000) * 100 = 10%.
Students often forget to divide the total interest by the number of years before calculating the percentage, leading to an incorrect result of 20%.
Identify given values
Extract the known parameters: Principal P=20000, Time T=2 years, and Simple Interest SI=4000.
P=20000,T=2,SI=4000
Rearrange interest formula
Use the standard simple interest formula SI=100P×R×T and isolate the rate of interest R.
R=P×TSI×100
Calculate the rate
Substitute the given values into the rearranged formula: R=20000×24000×100. Simplifying this gives 40000400000.
R=40000400000=10%
A is correct because the calculated annual rate of interest is 10%.
This concept is fundamental for financial mathematics and banking exams; similar logic applies to calculating compound interest if the time periods are annual.
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