Compound Interest Sum Calculation
The problem asks us to find the principal sum (P) when the compound interest (CI), rate (R), and time (T) are given. We are given:
- Compound Interest (CI) = ₹6,800
- Rate (R) = $12\frac{1}{2}\%$ per annum = 12.5% per annum
- Time (T) = 2 years
- Compounding is done annually.
Compound Interest Formula
The formula for compound interest is:
CI = P $\left[ \left(1 + \frac{R}{100}\right)^T - 1 \right]$
Where:
- P = Principal sum
- R = Annual interest rate
- T = Time in years
Step-by-Step Calculation
- Convert Rate to Fraction: The rate R = 12.5% can be written as a fraction: $R = 12.5\% = \frac{12.5}{100} = \frac{125}{1000} = \frac{1}{8}$
- Calculate the Growth Factor: Calculate the term $(1 + \frac{R}{100})$: $1 + \frac{R}{100} = 1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8}$
- Calculate the Compounding Factor: Calculate $(1 + \frac{R}{100})^T$ for T=2 years: $\left(\frac{9}{8}\right)^2 = \frac{9^2}{8^2} = \frac{81}{64}$
- Calculate the Interest Factor: Find the value of $\left[ \left(1 + \frac{R}{100}\right)^T - 1 \right]$: $\frac{81}{64} - 1 = \frac{81 - 64}{64} = \frac{17}{64}$
- Solve for Principal (P): Substitute the known values into the CI formula: $6,800 = P \times \frac{17}{64}$
- Isolate P: Rearrange the equation to solve for P: $P = 6,800 \times \frac{64}{17}$
- Final Calculation: Perform the multiplication: $P = (6,800 \div 17) \times 64$ $P = 400 \times 64$ $P = 25,600$
Conclusion
The principal sum on which the compound interest will be ₹6,800 is ₹25,600. This corresponds to Option B.
Similar Questions
- There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹10,000 after 3 years at the same rate?
- The difference between the compound interest and the simple interest accrued, at the same rate of interest, on an amount of ₹16,000 in 2 years was ₹1,000. What was the rate of interest percent per annum?
- A deposited ₹8,000 in a bank at 8% per annum simple interest. B deposited ₹6,000 at 10% compound interest per annum. After 3 years the difference between their interest will be:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
- Find the compound interest on ₹1,200 at 12% p.a. for 6 months compounded quarterly.
- A sum of money was lent on compound interest. It became ₹500 at the end of the first year and ₹550 at the end of second year. Find the rate of compound interest per annum.
- Simple interest on a sum of money, at $5\%$ per annum for 2 years, is ₹50. The compound interest on the same sum for the same period at the same interest rate is:
- If a sum on compound interest becomes 4 times in 3 years, then with the same interest rate, the sum will become 64 times in:
- If the difference between the compound interest and the simple interest on a certain sum of money at 8 % p.a. for 2 years is ₹240, then the sum of money is:
- The compound interest on a sum of ₹7,500 for 2 years at 4 % p.a. is
Important Questions from Simple and Compound Intrest
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is?
A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years does the same amount becomes Rs. 8000?
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, the compound interest on the same at the same rate and for the same time is:
- Amit invested the same sum at simple and compound interest (compounded annually) for 2 years at 4% per annum. The difference between the compound interest and the simple interest is ₹47. Find the sum (in ₹) invested in each case.
- Amit invested equal amounts at simple interest and compound interest, compounded annually, for 2 years at the same rate of 4% per annum. In the end, he found a difference of ₹53 between the two interests earned. What was the amount (in ₹) invested in each case?
