To find the compound interest, we first need to calculate the total amount after the specified period.
Compound Interest Calculation Steps
- Principal (P): ₹1,200
- Annual Interest Rate (R): 12% p.a.
- Time Period (T): 6 months
- Compounding Frequency: Quarterly
Adjusting Rate and Time for Quarterly Compounding
Since the interest is compounded quarterly, we need to adjust the annual rate and the time period:
- Rate per quarter (r): $\frac{\text{Annual Rate}}{4} = \frac{12\%}{4} = 3\%$ or $0.03$
- Number of quarters (n): The time period is 6 months. Since there are 4 quarters in a year, 6 months equals $0.5$ years. Therefore, the number of compounding periods is $0.5 \times 4 = 2$ quarters.
Calculating the Amount (A)
The formula for the amount (A) when compounded is:
$A = P \times (1 + r)^n$
Substitute the values:
$A = 1200 \times (1 + 0.03)^2$
$A = 1200 \times (1.03)^2$
$A = 1200 \times 1.0609$
$A = 1273.08$
Calculating the Compound Interest (CI)
The compound interest is the difference between the final amount and the principal amount:
$CI = A - P$
$CI = ₹1273.08 - ₹1200$
$CI = ₹73.08$
The compound interest is ₹73.08.
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.
- 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
The difference between the compound interest and the simple interest on a principal sum of $₹24,000$ in $2$ years at same rate of interest is $₹60$. The rate of interest 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?
