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.
Similar Questions
A sum of money, on compound interest, amounts to ₹5,290 in 2 years and to ₹6,083.50 in 3 years. If interest is compounded annually, then the rate of interest per annum is:
If a sum of money doubles itself in 10 years on compound interest, then in how many years will it become 16 times itself at the same rate of interest?
A sum of money, on compound interest, amounts to ₹578.40 in 2 years and to ₹614.55 in 3 years. The rate of interest per annum, in case of annual compounding, is:
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Important Questions from Compound Interest
A person borrowed Rs. 10000 on compound interest at the rate of 40 percent per annum. If the interest is compounded half yearly, then what will be the amount to be paid after 1.5 years?
The difference between the compound interest (compounding annually) and the simple interest on a sum of money at the rate of 40 per cent per annum for 2 years is Rs. 2400. What is the amount?
In how many years will a sum of Rs.1875 amount to Rs.2187 at 8 percent p.a. compound interest?
A sum of money has increased by 45% in 9 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
At a certain rate of compound interest a certain sum amounts to Rs. 64800 in 4 years and Rs. 93312 in 6 years. What is the compound interest earned in fifth year?
