A person loses 12.5% of his money and spends 60% of the remaining money. The part of his total money, now left with him, if deposited in a bank for 2 years at 8% annual simple interest, gives â¹2,030 after 2 years. What was the total initial amount of money with the person?

Points to Remember:

This is a mathematical word problem requiring a step-by-step solution.
The problem involves calculating percentages, simple interest, and working backward from a final amount.

Introduction:

This question is a mathematical word problem that tests the ability to solve multi-step problems involving percentages and simple interest. The problem presents a scenario where an individual loses a portion of their money, spends a further percentage, and then deposits the remaining amount in a bank. We are given the final amount after simple interest accrual and need to determine the initial amount of money. Understanding percentages and simple interest calculations is crucial to solving this problem. The formula for simple interest is: Simple Interest (SI) = (Principal Ã Rate Ã Time) / 100.

Body:

1. Calculating the Remaining Amount After Spending:

Let’s denote the initial amount of money as ‘x’.
The person loses 12.5% of his money, meaning he retains 100% – 12.5% = 87.5% of his money. This remaining amount is 0.875x.
He then spends 60% of this remaining amount, leaving him with 40% (100% – 60% = 40%). Therefore, the amount left is 0.40 * 0.875x = 0.35x.

2. Calculating the Principal Amount Deposited:

This 0.35x is the principal amount deposited in the bank.

3. Calculating the Principal Using Simple Interest:

The simple interest earned in 2 years at 8% annual rate is â¹2030. We can use the simple interest formula to find the principal amount:

SI = (P * R * T) / 100
2030 = (0.35x * 8 * 2) / 100
2030 = 0.56x
x = 2030 / 0.56
x â 3625

Therefore, the principal amount deposited (0.35x) is approximately 0.35 * 3625 = â¹1268.75

4. Verifying the Calculation:

Simple Interest on â¹1268.75 for 2 years at 8% = (1268.75 * 8 * 2) / 100 = â¹203. This is not equal to â¹2030. There’s a mistake in the calculation. Let’s revisit step 3.

The amount after interest is the principal plus the interest. So:
Principal + Interest = 2030
0.35x + (0.35x * 8 * 2)/100 = 2030
0.35x + 0.56x = 2030
0.91x = 2030
x = 2030 / 0.91
x â 2230.77

Therefore, the initial amount of money was approximately â¹2230.77.

Conclusion:

By systematically working backward from the final amount after simple interest, we determined that the initial amount of money with the person was approximately â¹2230.77. This problem highlights the importance of understanding percentage calculations and the application of the simple interest formula. It emphasizes the need for careful and methodical problem-solving, ensuring each step is accurately calculated to arrive at the correct answer. Financial literacy, including understanding simple interest and percentage calculations, is crucial for responsible financial management. Further education on financial planning can empower individuals to make informed decisions about their finances.