# compounding interest

Mike deposits x dollars in a bank to open an account that earns 10% interest compounded annually. All interest earned is immediately deposited into the account. Exactly two years later Donna deposits x dollars in the same bank to open an identical account. After the initial deposit, Mike and Donna make no additional deposits/withdrawals. Assume that when her account is 10 years old, Donna has $10000 in it. How much money is in Mike's account at this time? I have no idea how they get 12,100 for this problem. • Aug 25th 2010, 02:57 PM pickslides Have you seen this formula?$\displaystyle \displaystyle A = P e^{rt}$• Aug 25th 2010, 03:06 PM skeeter Donna's account after 10 yrs ...$\displaystyle 10000 = x(1.1)^{10}
$Mike's account after 12 years, let$\displaystyle A$= amount in his account at that time ...$\displaystyle A = x(1.1)^{12}$divide the last equation by the first ...$\displaystyle \displaystyle \frac{A}{10000} = \frac{x(1.1)^{12}}{x(1.1)^{10}}\displaystyle \displaystyle \frac{A}{10000} = (1.1)^2\displaystyle A = 10000(1.1)^2 = 12100\$