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The simple interest on a sum of money for 3 years at 5% per annum is Rs. 1200. What is the compound interest on the same sum for 2 years at the same rate?
Rs. 820
Rs. 800
Rs. 840
Rs. 810
Rs. 820
Simple Interest (SI) remains constant every year, allowing us to find the principal amount from the given 3-year interest. Using the principal, we then calculate the Compound Interest (CI) for 2 years at the same 5% rate per annum.
Simple Interest (SI) remains constant every year, allowing us to find the principal amount from the given 3-year interest. Using the principal, we then calculate the Compound Interest (CI) for 2 years at the same 5% rate per annum.
Simple interest is like a fixed rental fee paid every month, whereas compound interest is like a snowball rolling down a hill, gathering moss (interest on interest) as it grows larger each year.
SI is straight line, CI is curve growth!
SI=100P├Чr├ЧtтАЛ тАФ Calculates Simple Interest
CI=P├Ч(1+100rтАЛ)tтИТP тАФ Calculates Compound Interest
First, the principal P is determined using the Simple Interest formula SI=100P├Чr├ЧtтАЛ. With SI=1200, r=5, and t=3, we find P=5├Ч31200├Ч100тАЛ=8000. Next, the compound interest for 2 years is calculated using the formula A=P├Ч(1+100rтАЛ)t and CI=AтИТP.
Simple interest is calculated uniformly on the initial principal every year.
Compound interest includes interest earned on previously accumulated interest.
For 1 year, simple interest and compound interest are always equal.
Quick method to find principal using linear proportionality of SI
Failure to account for compounding in the first step leads to calculation errors
Banking and financial mathematics problems in competitive exams
Loan and investment growth evaluations
Principal amount calculated is Rs. 8000.
Option B (Rs. 800) represents the simple interest for 2 years, not compound interest.
A is correct тАФ The compound interest on the sum of Rs. 8000 for 2 years at 5% per annum is Rs. 820.
Always isolate the principal amount first from simple interest data before applying compound interest growth formulas.