Final answer:
The person will gain Rs 801.56 after lending out Rs 16,000 at 12.5% compound interest for 3 years which was initially borrowed at the same rate but simple interest. The gain is the difference between the compound interest received from the shopkeeper and the simple interest paid to the bank.
Step-by-step explanation:
The question asks how much a person will gain after lending out money at compound interest that was borrowed at simple interest. The borrowed amount is Rs 16,000 at a rate of 12.5% per annum. First, let's calculate the simple interest the person has to pay for borrowing the money. Simple interest (SI) is calculated using the formula: SI = P * R * T / 100, where P is the principal amount, R is the rate of interest per annum, and T is the time period in years.
For the borrowed amount:
- P = Rs 16,000
- R = 12.5%
- T = 3 years
SI = Rs 16,000 * 12.5 * 3 / 100 = Rs 6,000
Now, for the compound interest (CI) that the person will receive, we use the formula: A = P * (1 + R/100)^T, where A is the amount after T years. We need to calculate A and then determine the CI by subtracting the principal.
For the lent amount:
- P = Rs 16,000
- R = 12.5%
- T = 3 years
A = Rs 16,000 * (1 + 12.5/100)^3 approximately equals Rs 22,801.56
CI = Total amount - Principal = Rs 22,801.56 - Rs 16,000 = Rs 6,801.56
The gain after 3 years is the difference between CI and SI:
Gain = CI - SI = Rs 6,801.56 - Rs 6,000 = Rs 801.56
After converting the gain to the nearest option provided in the question, we can conclude: