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 ₹20,000 is borrowed by Heena for 2 years at an interest of 8% compounded annually. Find the compound interest.
- 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 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.
- An amount doubles itself at compound interest in five years. In how many years will it amount to sixteen times itself?
- How much amount of money (in ₹) at compound interest will amount to ₹5,000 in 3 years if the rate of interest is 2% for the $1^\text{st}$ year, 3% for the $2^\text{nd}$ year and 4% for the $3^\text{rd}$ year?
Find the total amount (in ₹) on ₹4500 at 12% per annum for 2 years and 8 months compounded annually.
- A sum of money, when invested at 10% compound interest per annum, amounts to ₹1,815 after 2 years. What is the original sum that was invested in the beginning?
A sum of money becomes $₹6,400$ in $2\text{ years}$ and $₹8,100$ in $4\text{ years}$ on compound interest. Find the rate of compound interest.
- Find the compound interest on ₹7,500 at 4% per annum for 2 years.
- The compound interest on ₹20,000 at 8% per annum is ₹3,328. The period in years is:
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?
