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What sum of money will yield 1,200 as simple interest in 4 years at 5% per annum?
4,000
5,000
6,000
7,000
6,000
Given: Simple Interest (SI) = 1,200, Time (T) = 4 years, Rate (R) = 5% per annum.
Simple Interest (SI) = 1,200, Time (T) = 4 years, Rate (R) = 5% per annum.
SI=100P├ЧR├ЧTтАЛ
Effective interest rate over 4 years is 4├Ч5%=20%. Since 20% of Principal equals 1,200, then 100% of Principal is 1,200├Ч5=6,000.
Students often mistake the Simple Interest for the Total Amount (A=P+SI) and subtract interest from the final value instead of solving for P directly.
Identify given variables
List the variables from the problem statement: SI=1200, T=4, and R=5%.
SI=1200,T=4,R=5
Rearrange the formula to solve for Principal
Isolate P in the formula SI=100P├ЧR├ЧTтАЛ to get P=R├ЧTSI├Ч100тАЛ.
P=5├Ч41200├Ч100тАЛ
Calculate the final sum
Substitute the values: P=20120000тАЛ=6000.
P=6000
C is correct because the calculated principal amount required to yield 1,200 interest under the given conditions is 6,000.
This concept is foundational for Profit and Loss questions, where the interest rate can be compared to profit percentage relative to the cost price.