According to top security experts there is only one way to fully Guarantee your data is safe. that is a bullet from a high powered rifle through the disks. I have heard that large government agencies in the US will not part with a hard drive no matter how many times it is formatted or supposedly securely erased as you never fully trust you will remove every piece of important data. if someone with enough time and know how wants your information they will retreive it.
Seeing as this computer is remaining in the family i cannot see it causing too many problems though. Do a secure erase of the disk using one of the above suggested programs and hopefully all should be fine. if i was disposing of the computer i always remove the hard drive before disposing of the box especially if it has been used as in your case for financial transactions.