Prove segment de is parallel to segment ab

That's a general triangle in size and shape so this will be a coordinate proof that for any triangle the segment between the midpoint of two sides is parallel to the third side.

Descartes didn't like the cleverness required to do Euclid-like geometry proofs and invented this method (using a coordinate grid) to turn geometry into algebra which is then indeed rather mechanically solved.

Parallel lines have the same slope. The slope of AB is obviously zero, but we calculate it as change in y over change in x, so

Similarly,

(Both slopes require which is necessary but not sufficient to have a real (non-degenerate) triangle.)

We have equal slopes so parallel line segments and a completed proof.

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of

it is 10.6 according to my calculations