The problem asks us to find the principal sum (P) given the interest earned specifically during the second year on a compound interest basis and the annual interest rate (R).
Understanding Compound Interest for the 2nd Year
The interest earned in the second year is the compound interest calculated on the amount accumulated after the first year. The formula for the amount after 1 year is \(A_1 = P \times (1 + R/100)\), where P is the principal sum and R is the annual interest rate.
The interest for the second year (CI_2nd_Year) is calculated on this amount \(A_1\) at the rate R:
CI_2nd_Year = \(A_1 \times (R/100)\)
Substituting the expression for \(A_1\):
CI_2nd_Year = \([P \times (1 + R/100)] \times (R/100)\)
Calculation Steps
- Identify Given Values:
- Interest earned in the 2nd year (CI_2nd_Year) = ₹3072
- Annual interest rate (R) = 20%
- Apply the Formula:
Using the formula derived above:
₹3072 = \([P \times (1 + 20/100)] \times (20/100)\)
₹3072 = \([P \times (1 + 0.20)] \times 0.20\)
₹3072 = \([P \times 1.20] \times 0.20\)
- Solve for the Principal Sum (P):
₹3072 = \(P \times (1.20 \times 0.20)\)
₹3072 = \(P \times 0.24\)
Now, isolate P:
\(P = ₹3072 / 0.24\)
\(P = ₹307200 / 24\)
\(P = ₹12800\)
Conclusion
The principal sum is ₹12800.
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?
