Mary recently graduated from college and got her MD degree to practice medicine. She quickly got a very good job at her local Hospital. But she finished college with a student loan of $50,000. She recently agreed with her local Bank that she would pay off her loan in 10 years, beginning at the end of the year. She also agreed that she would double her payments each and every year until her loan is paid off in full. Her student loan bears an interest rate of 5% compounded annually. What would be Mary's initial loan payment? Thanks for any help.
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.
