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How long will it take for 2,000 to become 2,600 at a rate of 10% per annum simple interest?
2 years
3 years
4 years
5 years
3 years
Calculate the interest gain as a percentage of the principal. 600 is 30% of 2,000. Since the annual rate is 10%, the time required is 30%/10%=3 years.
Principal P = 2,000, Final Amount A = 2,600, Rate R = 10% per annum.
SI=AтИТP=100P├ЧR├ЧTтАЛ
Calculate the interest gain as a percentage of the principal. 600 is 30% of 2,000. Since the annual rate is 10%, the time required is 30%/10%=3 years.
Students often mistake the final amount 2,600 for the simple interest and calculate T=(2600├Ч100)/(2000├Ч10), which is incorrect.
Calculate Simple Interest
Subtract the principal from the final amount to find the total simple interest accrued: 2,600тИТ2,000=600.
SI=2600тИТ2000=600
Rearrange Formula for Time
Using the formula SI=(P├ЧR├ЧT)/100, solve for T as T=(SI├Ч100)/(P├ЧR).
T=P├ЧRSI├Ч100тАЛ
Substitute Values
Plug in the known values: P=2,000, SI=600, and R=10.
T=2000├Ч10600├Ч100тАЛ
Final Calculation
Simplify the fraction to get T=60,000/20,000=3.
T=3┬аyears
B is correct because the simple interest of 600 on a principal of 2,000 at 10% rate results in exactly 3 years.
This concept is foundational for Compound Interest problems; always differentiate between simple interest (constant) and compound interest (compounding annually).
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