Calculating Time for Compound Interest (Half-Yearly)
This problem requires finding the time period for an investment to grow from a principal amount to a future amount at a given interest rate, compounded half-yearly.
Identify Given Values
- Principal Amount ($P$): ₹ 4400
- Amount ($A$): ₹ 4576
- Annual Interest Rate ($R$): 8% per annum
- Compounding Frequency: Half-yearly
Adjust Rate and Calculate Periods
Since interest is compounded half-yearly, we need to adjust the rate and determine the number of compounding periods ($n$).
- Rate per period ($r$): $\frac{8\%}{2} = 4\%$ or $0.04$
- The number of periods ($n$) is what we need to find.
Apply Compound Interest Formula
The formula for compound amount is $A = P(1 + r)^n$. Substitute the known values:
$4576 = 4400(1 + 0.04)^n$
Solve for Number of Periods (n)
- Divide both sides by the principal amount:
$\frac{4576}{4400} = (1.04)^n$
- Simplify the fraction:
$1.04 = (1.04)^n$
- Equate the exponents:
$n = 1$
This means there is 1 compounding period.
Determine Total Time
Since the compounding is half-yearly, each period is 6 months.
- Total Time = Number of periods ($n$) × Duration of each period
- Total Time = $1 \times 6$ months
- Total Time = 6 months
Therefore, it will take 6 months for ₹ 4400 to become ₹ 4576 at 8% per annum compounded half-yearly.
Important Questions from Compound Interest
At what rate percent per annum will Rs. 7200 amount to Rs. 7938 in one year, if interest is compounded half yearly?
What is the compound interest (in Rs.) on a sum of Rs. 8192 for \(1 \frac{1}{4}\) years at 15% per annum, if interest is compounded 5-monthly ?
What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
A sum invested at compound interest amounts to Rs. 7,800 in 3 years and Rs. 11,232 in 5 years. What is the rate per cent?
