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If a sum of Rs 8,000 amounts to Rs 9,261 in 3 years at compound interest compounded annually, find the rate of interest per annum.
5%
10%
8%
12%
5%
Compound interest is calculated on the principal amount as well as the accumulated interest of previous periods. For a principal of Rs 8,000 amounting to Rs 9,261 in 3 years, the annual rate of interest is 5%.
Compound interest is calculated on the principal amount as well as the accumulated interest of previous periods. For a principal of Rs 8,000 amounting to Rs 9,261 in 3 years, the annual rate of interest is 5%.
Think of compound interest like bacterial growth or a snowball rolling downhill, where each layer adds to the base size, causing exponential acceleration over successive time intervals.
P-R-N: Principal, Rate, Number of yearsтАФmultiply the growth factor year by year.
A=P(1+100RтАЛ)n тАФ Amount formula under compound interest
CI=AтИТP тАФ Compound interest earned
The growth of money under compound interest follows an exponential geometric progression governed by the formula A=P(1+100RтАЛ)n. By substituting the given principal, amount, and time period, the equation simplifies to taking the cube root of the amount-to-principal ratio, allowing the exact rate percentage to be isolated.
Compound interest grows exponentially compared to simple interest.
The ratio of the amount to the principal gives the cube of the annual growth factor for a 3-year period.
Yields higher returns over long periods compared to simple interest due to the compounding effect.
Calculations can become complex and non-linear over irregular time periods.
Banking loans and fixed deposits
Population growth models and financial forecasting
Standard base values: The cube of 21 is 9261 and the cube of 20 is 8000.
Option B (10%), Option C (8%), and Option D (12%) yield incorrect final amounts when compounded over 3 years.
A is correct тАФ The annual rate of interest calculated using the compound interest formula is 5%.
Always look for perfect squares or cubes when time is 2 or 3 years to quickly solve compound interest problems without heavy algebraic expansion.
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