Calculating Profit from Simple vs. Compound Interest Transaction
This problem involves calculating the profit made from a financial transaction where a principal amount is borrowed at a simple interest rate and then lent out at a compound interest rate. We need to find the difference between the interest earned (compound) and the interest paid (simple) over the specified period.
Simple Interest (SI) Calculation
First, let's calculate the simple interest A has to pay to B.
The formula for Simple Interest is:
$$SI = \frac{P \times R \times T}{100}$$Where:
- P = Principal amount = $₹58,000$
- R = Rate of interest per annum = 8%
- T = Time period in years = 2 years
Plugging the values into the formula:
$$SI = \frac{58000 \times 8 \times 2}{100}$$ $$SI = 580 \times 16$$ $$SI = ₹9,280$$So, A pays $₹9,280$ as simple interest to B.
Compound Interest (CI) Calculation
Next, let's calculate the amount A receives from C using compound interest.
The formula for the Amount (A) compounded annually is:
$$A = P \left(1 + \frac{R}{100}\right)^T$$Where:
- P = Principal amount = $₹58,000$
- R = Rate of interest per annum = 10%
- T = Time period in years = 2 years
Calculating the total amount received after 2 years:
$$A = 58000 \left(1 + \frac{10}{100}\right)^2$$ $$A = 58000 \left(1 + 0.1\right)^2$$ $$A = 58000 \left(1.1\right)^2$$ $$A = 58000 \times 1.21$$ $$A = ₹70,180$$Now, we calculate the compound interest earned by A:
$$CI = \text{Amount} (A) - \text{Principal} (P)$$ $$CI = 70180 - 58000$$ $$CI = ₹12,180$$So, A earns $₹12,180$ from C as compound interest.
Profit Earned in Transaction
The profit earned by A is the difference between the compound interest received from C and the simple interest paid to B.
Profit = CI - SI
Profit = $12,180 - 9,280$
Profit = $₹2,900$
Therefore, A earned $₹2,900$ in the transaction at the end of 2 years.
Similar Questions
- What is the difference (in ₹, to the nearest rupee) between the simple interest and compound interest on ₹24,500 in two years at the rate of 8% per annum? The compound interest is compounded annually.
- What is the difference between the compound interest and simple interest (in ₹, to the nearest integer) on ₹12,000 in 2 years at 8% per annum, compounded annually?
- The simple interest on a sum of money at 10% per annum for 2 years is ₹8,000. What will be the compound interest (in ₹) on the same sum for the same period at the same rate compounded annually?
- The difference between the interest compounded annually and the simple interest on a sum of ₹31,250 for 2 years at 8% per annum is:
- The difference between the compound interest and simple interest on $x$ at a rate of 8.5% per annum for 2 years is ₹260.10. What is the value of $x$?
The difference between the compound interest and simple interest for the amount ₹5,000 in 2 years is ₹50. 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:
