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
- If the interest earned during the $2^{\text{nd}}$ year on a certain sum is ₹6,258, and the rate of interest is 20% per annum compounded annually, then the sum is:
- The difference between compound interest and simple interest, at the same rate, on an amount of ₹15,000 for 2 years is ₹24. What is the rate of interest per annum?
- 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?
- 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:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
- 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 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.
- 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:
- 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:
Important Questions from Simple and Compound Intrest
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is ₹797. Find the sum (rounded off to the nearest integer).
- The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 10% per annum is $₹407$. Find the sum [rounded off to the nearest integer].
The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 17% per annum is ₹967. Find the sum [rounded off to the nearest integer].
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
