Question: Assume that you collect P dollars from this transaction and being a mathematics wiz, you have developed another formula to calculate the future value of your investment:

where, r is the rate of interest and t is the time horizon.

Suppose you invest your profit, P dollars, from above transaction, and invest it in a bank at 5% rate of interest for 7 years.

What will be the Future Value of this investment after 7 years? Find out dF/dt, assuming P and r are constant. In terms of money, what does dF/dt represent? Also, find out dF/dr, assuming P and t are constant. In terms of money, what does dF/dr represent?