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The simple interest on a certain sum for 3 years at 8% per annum is Rs 1200. The compound interest on the same sum for 2 years at the same rate is:
Rs 832
Rs 816
Rs 840
Rs 800
Rs 832
The correct answer is Option A (Rs 832). First, the principal sum is determined using the simple interest formula, yielding Rs 5000. Then, this principal is used to calculate the compound interest for 2 years at the same rate of 8% per annum.
The correct answer is Option A (Rs 832). First, the principal sum is determined using the simple interest formula, yielding Rs 5000. Then, this principal is used to calculate the compound interest for 2 years at the same rate of 8% per annum.
Simple interest is like a flat rental fee where you pay the same amount every month, while compound interest is like a snowball rolling downhill, gathering more snow (interest) with each turn.
SI=100P├Чr├ЧtтАЛ тАФ Simple interest formula
CI=P(1+100rтАЛ)tтИТP тАФ Compound interest formula
Simple interest is calculated uniformly on the principal amount over time, whereas compound interest calculates interest on the accumulated amount (principal plus previous interest). By first determining the principal P=r├ЧtSI├Ч100тАЛ, we can apply the compound interest formula CI=P(1+100rтАЛ)tтИТP to find the total interest over 2 years.
Simple interest remains constant for every year because it is calculated only on the initial principal.
Compound interest grows exponentially because interest is earned on both the principal and previously accumulated interest.
Banking calculations
Loan and investment planning
For 2 years, the effective compound interest rate can also be calculated using the successive percentage formula: r+r+100r2тАЛ. For 8%, it is 8+8+10064тАЛ=16.64%.
Option B (Rs 816), Option C (Rs 840), and Option D (Rs 800) represent incorrect calculations or misinterpretations of the compounding effect.
A is correct тАФ The compound interest on Rs 5000 for 2 years at 8% per annum is Rs 832.
For a 2-year period, remember the difference between CI and SI is given by the formula CIтИТSI=P(100rтАЛ)2, which is useful for quick cross-verification in competitive exams.