Calculate Annual Compound Interest Rate
The question asks to find the annual rate of interest based on an initial investment and its value after one year, with interest compounded annually. The total investment duration of three years is extra information not needed to find the rate.
Step-by-Step Calculation
- Identify the given values:
- Principal amount ($P$) = ₹5,000
- Amount after 1 year ($A_1$) = ₹5,600
- Time period ($t$) = 1 year
- Use the compound interest formula for one year: $A_1 = P(1 + r)^t$, where $r$ is the annual interest rate.
- Since $t=1$, the formula simplifies to $A_1 = P(1 + r)$.
- Substitute the known values into the formula:
₹5,600 = ₹5,000 (1 + r)
- Solve for $r$:
- Divide both sides by ₹5,000: $1 + r = \frac{5600}{5000}$
- Simplify the fraction: $1 + r = \frac{56}{50} = \frac{28}{25}$
- Convert the fraction to a decimal: $1 + r = 1.12$
- Isolate $r$: $r = 1.12 - 1$ $r = 0.12$
- Convert the rate $r$ from decimal to percentage:
$Rate\% = r \times 100\% = 0.12 \times 100\% = 12\%$
Therefore, the rate of interest per annum is 12%.
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 man placed a fixed deposit of ₹16,000 for a period of 2 years at 10% compound interest. If the interest is compounded half-yearly, then how much amount (in ₹) will he receive after the full term?
- 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:
- A sum is invested at compound interest payable annually. The interest in two successive years was ₹225 and ₹236.25. Find the rate of interest.
- 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:
- A sum was invested for 3 years on compound interest at 6%, 12% and 18% in first, second and third year respectively. The sum amounts to ₹20,000 in 3 years. Find the principal amount.
- 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.
- The population of a town increases at the rate of 10% every year. The present population is 1,000. In how many years will the population become 1,331?
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?
