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What sum of money will amount to ₹1,116 at 4% per annum simple interest in 6 years?
₹800
₹900
₹700
₹1,000
₹900
Calculate the effective percentage interest: R×T=4%×6=24%. The amount is 124% of the principal, so 1.24×P=1116, which simplifies to P=1116/1.24=900.
Amount (A) = ₹1,116, Rate (R) = 4% per annum, Time (T) = 6 years.
A=P(1+100R×T)
Calculate the effective percentage interest: R×T=4%×6=24%. The amount is 124% of the principal, so 1.24×P=1116, which simplifies to P=1116/1.24=900.
Confusing 'Amount' (Principal + Interest) with 'Principal', leading students to calculate simple interest on ₹1,116 instead of using the amount formula.
Define the relationship
The formula relating Amount (A), Principal (P), Rate (R), and Time (T) in Simple Interest is A=P+SI, where SI=100P×R×T.
A=P(1+100R×T)
Substitute given values
Substitute A=1116, R=4, and T=6 into the formula to find P.
1116=P(1+1004×6)
Simplify and solve for P
Calculate the inner bracket: 1+10024=1.24. Then divide the total amount by 1.24 to isolate P.
1116=P(1.24)⟹P=1.241116=900
B is correct because the principal amount calculation P=1116/1.24 results in exactly ₹900.
This concept is foundational for Compound Interest and Installment payment problems, where the rate compounding adds complexity to the base algebraic structure.
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