Compound Interest Rate Calculation
This problem involves calculating the annual rate of compound interest using the amounts at two different time points.
Understanding Compound Interest Amounts
Let the principal sum be 'P' and the annual rate of interest be 'r'. The formula for the amount (A) after 't' years with compound interest compounded annually is:
$ A = P(1 + r)^t $We are given:
- Amount after 2 years ($A_2$) = Rs. $1,600$
- Amount after 3 years ($A_3$) = Rs. $2,000$
Using the formula:
- $ 1600 = P(1 + r)^2 \quad \quad (1) $
- $ 2000 = P(1 + r)^3 \quad \quad (2) $
Finding the Rate of Interest
To find the rate 'r', we can divide the second equation by the first equation:
$ \frac{2000}{1600} = \frac{P(1 + r)^3}{P(1 + r)^2} $Simplify the equation:
$ \frac{5}{4} = (1 + r) $Now, solve for 'r':
$ 1 + r = 1.25 $ $ r = 1.25 - 1 $ $ r = 0.25 $Convert the rate to a percentage:
$ \text{Rate} = r \times 100\% = 0.25 \times 100\% = 25\% $Therefore, the rate of interest is 25%.
Similar Questions
- What is the compound interest on a sum of Rs. 12,500 at 15% p.a. in 2 years, if the interest is compounded 8-monthly?
- A certain amount increases to five times its initial value after 10 years of compounding interest. How many years will it take for it to grow to twenty-five times its original amount?
- A vendor lends 74,000 rupees at a rate of 12% compound interest per annum, compounded annually. Find the interest for the 3rd year.
- A sum of money invested at compound interest amounts to twice itself in 4 years. In how many years will it become 8 times itself?
- What is the compound interest on Rs. 8000 for 2 year at 10% per annum?
- The compound interest on a certain sum for 3 years at 20% per annum is ₹864. Find the simple interest on the same sum at the same rate and period.
- What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 10% p.a.?
A sum of money becomes three times itself in 3 years at compound interest.
What is the rate of interest?
- If the amount is Rs. 600 and the Principal is Rs. 450, which is compounded yearly for 1 year, calculate the rate of interest.
- What will be the amount to be paid at the end of 5 years on Rs. 4500 at 10% per annum compounded annually?
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?
