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Unformatted text preview: oney increases.6
We have observed that the more times you compound the interest per year, the more money you
will earn in a year. Let’s push this notion to the limit.7 Consider an investment of $1 invested
at 100% interest for 1 year compounded n times a year. Equation 6.2 tells us that the amount of
money in the account after 1 year is A = 1 + n . Below is a table of values relating n and A.
≈ 2.7182 As promised, the more compoundings per year, the more money there is in the account, but we
also observe that the increase in money is greatly diminishing. We are witnessing a mathematical
‘tug of war’. While we are compounding more times per year, and hence getting interest on our
interest more often, the amount of time between compoundings is getting smaller and smaller, so
there is less time to build up additional interest. With Calculus, we can show8 that as n → ∞,
A = 1 + n → e, where e is the natural base ﬁrst presented in Section 6.1. Taking...
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