# compounding interest

• Aug 25th 2010, 03:30 PM
donnagirl
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, 03:57 PM
pickslides
Have you seen this formula?

$\displaystyle A = P e^{rt}$
• Aug 25th 2010, 04:06 PM
skeeter
Donna's account after 10 yrs ...

$10000 = x(1.1)^{10}
$

Mike's account after 12 years, let $A$ = amount in his account at that time ...

$A = x(1.1)^{12}$

divide the last equation by the first ...

$\displaystyle \frac{A}{10000} = \frac{x(1.1)^{12}}{x(1.1)^{10}}$

$\displaystyle \frac{A}{10000} = (1.1)^2$

$A = 10000(1.1)^2 = 12100$
• Aug 25th 2010, 04:36 PM
thegreenmathdr