Understanding the Compound Interest Problem
The question asks for the original principal sum (sum) based on the interest earned during the second year of compounding and the annual interest rate.
Given Information
- Interest for the 2nd year: ₹6,258
- Annual interest rate (R): 20%
- Interest is compounded annually.
- We need to find the principal sum (P).
Formula for Interest in the nth Year
For annual compounding, the interest earned specifically in the nth year is given by:
Interest in nth year = $ P \times \left(1 + \frac{R}{100}\right)^{n-1} \times \frac{R}{100} $
Here, $P$ is the principal, $R$ is the rate, and $n$ is the year.
Calculation Steps
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Substitute the values for the 2nd year ($n=2$):
₹6,258 = $ P \times \left(1 + \frac{20}{100}\right)^{2-1} \times \frac{20}{100} $
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Simplify the equation:
₹6,258 = $ P \times \left(1 + 0.20\right)^{1} \times 0.20 $
₹6,258 = $ P \times (1.20) \times 0.20 $
₹6,258 = $ P \times 0.24 $
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Solve for the principal sum ($P$):
$ P = \frac{₹6,258}{0.24} $
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Perform the division:
$ P = \frac{625800}{24} = ₹26,075 $
Therefore, the principal sum is ₹26,075.
Similar Questions
- The difference between compound interest and simple interest, at the same rate, on an amount of ₹15,000 for 2 years is ₹24. What is the rate of interest per annum?
- 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?
- Simple interest on a sum of money, at $5\%$ per annum for 2 years, is ₹50. The compound interest on the same sum for the same period at the same interest rate is:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
- 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?
- Find the compound interest on ₹1,200 at 12% p.a. for 6 months compounded quarterly.
- A sum of money was lent on compound interest. It became ₹500 at the end of the first year and ₹550 at the end of second year. Find the rate of compound interest 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:
- If a sum on compound interest becomes 4 times in 3 years, then with the same interest rate, the sum will become 64 times in:
- If the difference between the compound interest and the simple interest on a certain sum of money at 8 % p.a. for 2 years is ₹240, then the sum of money is:
Important Questions from Simple and Compound Intrest
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is ₹797. Find the sum (rounded off to the nearest integer).
- 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:
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 10% per annum is $₹407$. Find the sum [rounded off to the nearest integer].
The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 17% per annum is ₹967. Find the sum [rounded off to the nearest integer].
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
