# Using exponents

Now that you can easily find next year’s bank balance, let’s keep going for a few years:

2010: $1000

2011: $1000 × 1.05 = $1050

2012: $1000 × 1.05 × 1.05 = $1102.50

2013: $1000 × 1.05 × 1.05 × 1.05 = $1157.63

2014: $1000 × 1.05 × 1.05 × 1.05 × 1.05= $ 1215.51

You can see that by the year 2025 or so, this is going to get really cumbersome:

2025: $1000 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 × 1.05 = $2078.93

Of course there is an easier way to calculate the balance by the year 2025: instead of doing the multiplication 15 times, use an exponent: 1.05^{15}.

Hmm, use an exponent to calculate exponential growth. Coincidence…?

So, how much will you have by the year 2025?

How about 2050?

Incidentally, this is how you get a retirement account – do it now! (At least, do it when you graduate. In 40 years, you’ll thank me.)

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