Growth and time: compounding, doubling, arrival

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

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

772315.4473951627

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

9.930955714667654

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

1.687752907426951*^7

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

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