Growth and time: compounding, doubling, arrival

Workflow 5 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

balance[principal_, monthly_, rate_, months_] := principal (1 + rate)^months + monthly ((1 + rate)^months - 1)/rate

No output - this step sets something up for the next one.

Step 2

after30years = N[balance[20000, 500, 0.07/12, 360]]

Output

772315.4473951627

Step 3

doublingYears = N[Log[2]/(12 Log[1 + 0.07/12])]

Output

9.930955714667654

Step 4

N[D[balance[20000, 500, r/12, 360], r] /. r -> 0.07]

Output

1.687752907426951*^7

Step 5

Plot[balance[20000, 500, r/12, 360], {r, 0.02, 0.10}]

Output

-Graphics-

Functions used