The first part of your question is very simple. We simply find the PV of her 7 payments of $50,000 each @ 5% comp. annually=PV=$289,318.67. You use the common TVM formula to calculate this, which is:
PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD.
The second part is a little more involved. However, there is also a TVM formula to calculate it directly, which I'm sure is in your textbook. However, we may not need it in this case. Because, her father's monthly payments double every month for 12 months, then we can solve directly for the first payment. If we put the first payment as P, then we have:
P x 2^12=$289,318.67. Solve for P.
P=$289,318.67 / 2^12
P=$70.63. This should be his first payment minus interest. Since the interest he got was 10% comp. annually, we have to convert this to a monthly compound, which comes to about 9.57%. 9.57/(12 x 100) +1=1.007975. This is the monthly interest rate. We divide the above payment by this and we should get his initial deposit: $70.63/1.007975=$70.08, which is his initial deposit.