 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Victor purchased a penthouse for $200,000. The value of the penthouse depreciates to $145,800 after three years. Find the rate of depreciation. The compound interest formula is A is equal to P into 1 plus R upon 100 raise to power n. The value of growth factor is 1 plus R upon 100. The value of decay factor is 1 minus R upon 100. With this key idea, let us proceed with the solution. According to the question, we need to find the rate of depreciation if Victor purchased a penthouse for $200,000 and the value of the penthouse depreciates to $145,800 after three years. As we have to find the rate of depreciation, so let the depreciation rate be R% per annum. Given that time n is equal to three years as the value of the penthouse depreciates, therefore using the formula with decay factor, we have A is equal to P into 1 minus R upon 100 raise to power n where A is the value of the penthouse after three years and P is the present value of the penthouse. The value of the penthouse after three years is given to us as $145,800 and the present value of the penthouse is given to us as $200,000. So $145,800 is equal to $200,000 into 1 minus R upon 100 raise to power 3. This implies $145,800 upon $200,000 is equal to 1 minus R upon 100 raise to power 3. After cancelling the zeros, we have $1458 upon $2000 is equal to 1 minus R upon 100 raise to power 3, which implies $729 upon $1000 is equal to 1 minus R upon 100 raise to power 3. As $729 is the cube of 9 and $1000 is the cube of 10, so this becomes 9 upon 10 whole cube is equal to 1 minus R upon 100 raise to power 3. Taking the cube roots on both sides, this implies 9 upon 10 is equal to 1 minus R upon 100 which implies R upon 100 is equal to 1 minus 9 upon 10 which is equal to 10 minus 9 upon 10 which is equal to 1 by 10. So R is equal to 100 upon 10 which is equal to 10. This implies that rate of depreciation is equal to 10% per annum which is our answer. This completes our session. Hope you enjoyed the session.