 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that in how many years will $2,662 amount to $2,662 at 10% compound interest? The compound interest formula states that amount is equal to e into 1 plus r upon 100 raised to power m. With this key idea, let us proceed with the solution. According to the question, we need to find the time after which $2,662 amounts to $2,662 at 10% compound interest. So here, amount is equal to $2,662. The principal p is equal to $2,000 and the rate of interest r is equal to 10% per annum. As we know, amount is equal to p into 1 plus r upon 100 raised to power n where we need to find the time n and the amount and the principal are given. So $2,662 is equal to $2,000 into 1 plus 10 upon 100 raised to power n which implies $2,662 upon 2000 is equal to 1 plus 1 by 10 raised to power n which implies $2,662 upon 2000 is equal to 10 plus 1 upon 10 raised to power n which is equal to 11 upon 10 raised to power n. Now, $2 times $1,000 is $2,000 and $2 times $1,331 is $2,662. So this implies $1,331 upon 1000 is equal to 11 upon 10 raised to power n. As $1,331 is the cube of 11 and $1,000 is the cube of 10, this implies 11 upon 10 whole cube is equal to 11 upon 10 raised to power n which implies n is equal to 3. Hence, $2,000 will amount to $2,662 in 3 years which is our answer. This completes our session. Hope you enjoyed this session.