Simple Interest to Compound Interest Calculation
The question asks for the compound interest (CI) on a sum, given the simple interest (SI) details for the same sum, rate, and time period.
Calculate Principal from Simple Interest
First, we need to find the principal amount (P) using the given simple interest (SI), rate (R), and time (T).
- SI = ₹50
- Rate (R) = 5% per annum
- Time (T) = 2 years
The formula for Simple Interest is:
$ SI = \frac{P \times R \times T}{100} $
Substitute the given values:
$ 50 = \frac{P \times 5 \times 2}{100} $
$ 50 = \frac{P \times 10}{100} $
$ 50 = \frac{P}{10} $
Solve for P:
$ P = 50 \times 10 $
$ P = 500 $
The principal sum is ₹500.
Calculate Compound Interest
Now, we calculate the compound interest (CI) for the same principal, rate, and time.
- Principal (P) = ₹500
- Rate (R) = 5% per annum
- Time (T) = 2 years
The formula for Compound Interest is:
$ CI = P \left(1 + \frac{R}{100}\right)^T - P $
Substitute the values:
$ CI = 500 \left(1 + \frac{5}{100}\right)^2 - 500 $
$ CI = 500 \left(1 + 0.05\right)^2 - 500 $
$ CI = 500 \left(1.05\right)^2 - 500 $
Calculate the square of 1.05:
$ (1.05)^2 = 1.1025 $
Continue the calculation for CI:
$ CI = 500 \times 1.1025 - 500 $
$ CI = 551.25 - 500 $
$ CI = 51.25 $
The compound interest is ₹51.25.
Similar Questions
- There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹10,000 after 3 years at the same rate?
- The difference between the compound interest and the simple interest accrued, at the same rate of interest, on an amount of ₹16,000 in 2 years was ₹1,000. What was the rate of interest percent per annum?
- A deposited ₹8,000 in a bank at 8% per annum simple interest. B deposited ₹6,000 at 10% compound interest per annum. After 3 years the difference between their interest will be:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
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The difference between the compound interest and the simple interest on a principal sum of $₹24,000$ in $2$ years at same rate of interest is $₹60$. The rate of interest is:
Important Questions from Simple and Compound Intrest
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
- The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
