 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, in how much time will $625 amount to $729 at 8% per annum compound interest? We know that compound interest formula is amount A is equal to P into 1 plus R upon 100 raised to power N. With this key idea let us proceed with the solution. According to the question we need to find the time in which $625 amount to $729 at 8% per annum. Let the required time be N years. Let the principal be P which is equal to $625. Let the amount be A equal to $729. The rate of interest R is equal to 8% per annum. As we know amount A is equal to P into 1 plus R upon 100 raised to power N. So $729 is equal to $625 into 1 plus 8 upon 100 raised to power N. This implies $729 upon $625 is equal to 1 plus 8 upon 100 raised to power N. Which implies $729 upon $625 is equal to 100 plus 8 upon 100 raised to power N which is equal to 108 upon 100 raised to power N. Now $729 is the square of $27 and $625 is the square of $25. This implies $27 upon $25 raised to power 2 is equal to 108 upon 100 raised to power N. Now $425 is 100 and $427 is 108. So $27 upon $25 raised to power 2 is equal to $27 upon $25 raised to power N. This implies N is equal to 2. Hence time is equal to 2 years which is our answer. This completes our session. Hope you enjoyed this session.