A car depreciates at the rate of 10% every year. If the cost price of the car is ₹ 5,00,000, what will be the value of the car after 6 years ?

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We have a car depreciation problem. A car initially costs 5 lakh rupees and depreciates at a rate of 10 percent every year. We need to find its value after 6 years. This is an exponential decay problem where the car loses 10 percent of its current value each year. To solve depreciation problems, we use the exponential decay formula. The final value equals the initial value multiplied by one minus the rate, raised to the power of time. In our case, the final value equals 5 lakh rupees times 0.90 raised to the power of 6. Now let's calculate 0.90 to the power of 6 step by step. First, 0.90 squared equals 0.81. Then 0.90 to the fourth power equals 0.6561. Finally, 0.90 to the sixth power equals 0.531441. Multiplying this by 5 lakh rupees gives us the final answer of 2 lakh 65 thousand 720 rupees and 50 paise. This graph shows how the car's value decreases over time. Starting at 5 lakh rupees, it drops to 4.5 lakh after one year, then continues declining exponentially. After 6 years, the car is worth approximately 2 lakh 65 thousand 720 rupees and 50 paise, which is about 53% of its original value. In conclusion, after 6 years of 10% annual depreciation, the car originally worth 5 lakh rupees will be valued at 2 lakh 65 thousand 720 rupees and 50 paise. This represents a total depreciation of approximately 47% from its original value. This exponential decay model is commonly used in finance and accounting to calculate asset depreciation over time.