Compound Interest Calculation Steps
This problem involves calculating the final amount when interest is compounded half-yearly.
Given:- Principal (P) = ₹4000
- Annual Interest Rate (R) = 20%
- Time Period (T) = $\frac{3}{2}$ years = 1.5 years
- Compounding Frequency = Half-yearly
Adjusting Rate and Time for Half-Yearly Compounding
When interest is compounded half-yearly, we need to adjust the rate and the number of periods:
- Rate per period (r) = $\frac{\text{Annual Rate}}{2} = \frac{20\%}{2} = 10\% = 0.10$
- Number of periods (n) = Time in years $\times$ 2 = $\frac{3}{2} \times 2 = 3$
Calculating the Final Amount
The formula for the amount (A) with compound interest is:
$A = P \times (1 + r)^n$
Substitute the adjusted values:
- $A = 4000 \times (1 + 0.10)^3$
- $A = 4000 \times (1.1)^3$
- $A = 4000 \times 1.331$
- $A = 5324$
Therefore, the sum of ₹4000 will amount to ₹5324.
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:
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- 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?
- 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.
- 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:
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 ₹______.
