Congratulate Mary on her MD!. This is an interesting question but rather easy to solve.
There is a specific but relatively involved TVM formula to solve just this kind of financial problem, but I'm not going to use it!. Rather, I'm going to use a much simpler method to arrive at the answer.
Her payments will form a geometric series as follows: 1, 2, 4, 8.............512. Now, we can use cash flow analysis to find the PV of this series @ 5% comp. annually. Or we can sum them up on a good calculator or engine such Wolfram/ Alpha, which is a lot easier and faster. So, using summation on W/A would look like this: ∑[2^(n) / 1.05^(n+1)], n=0 to 9 =660.681233290.....etc.
Now we simply divide her loan of $50,000 / 660.681233290=$75.68 which will be Mary's first payment.
This amount will double each year for 10 years until the loan is paid off.
Here is W/A calculation for anybody interested:
http://www.wolframalpha.com/input/?i=%E2%88%91%5B2%5E(n)+%2F+1.05%5E(n%2B1)%5D,+n%3D0+to+9
And that is all there is to it.
I don't normally post simple math but ok
