Compound Interest Calculation for Fixed Deposit
This solution explains how to calculate the final amount received from a fixed deposit with half-yearly compound interest.
Problem Breakdown
- Principal Amount (P): ₹16,000
- Annual Interest Rate (R): 10%
- Time Period (T): 2 years
- Compounding Frequency: Half-yearly
Adjusting Parameters 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): The annual rate is divided by 2. $r = \frac{R}{2} = \frac{10\%}{2} = 5\% = 0.05$
- Number of periods (n): The time period in years is multiplied by 2. $n = T \times 2 = 2 \text{ years} \times 2 = 4 \text{ periods}$
Calculating the Final Amount
The formula for the amount (A) with compound interest is:
$ A = P \left(1 + r\right)^n $Substitute the adjusted values into the formula:
$ A = 16,000 \times (1 + 0.05)^4 $ $ A = 16,000 \times (1.05)^4 $First, calculate $(1.05)^4$:
$ (1.05)^4 \approx 1.21550625 $Now, calculate the final amount:
$ A = 16,000 \times 1.21550625 $ $ A = 19,448.10 $Result
The amount the man will receive after the full term is ₹19,448.10.
Similar Questions
- A sum of money doubles itself at a compound interest in 15 years. In how many years will it become 8 times the original amount?
- A sum of ₹15,625 amounts to ₹24,389 in 3 years at a certain rate of interest per annum, compounded annually. The rate of interest per annum is:
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- A sum of ₹20,000 is borrowed by Heena for 2 years at an interest of 8% compounded annually. Find the compound interest.
- The compound interest on ₹20,000 at 8% per annum is ₹3,328. The period in years is:
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- In what time will ₹ $1,000$ become ₹ $1,331$ at an interest rate of $10\%$ per annum compounded annually?
- Find the compound interest when the principle is ₹6,000 at an interest of 10% per annum for 2 years.
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- If an investment of ₹1,000 amounts to ₹1,440 in 2 years when compounded annually, then what is the rate of compound interest?
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?
