Teaching Kids Programming – Compound Interests and Euler’s number (Math Constant E)

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Suppose you have deposited $1 into the bank account, and if the interest rate is 100% (AER = Annual Equivalent Rate).

If the interests are paid out once yearly, together with $1 (your initial money, also called principal balance), you will have $1+$1=$2.

However, if the interests are paid out twice e.g. every 6 months, you will get slightly more: the interests earned at first 6 months contribute to the principal balance in the second 6 months.

If we tend to increase the number of interests paid, we tend to get a larger overall payout (principal and the accumulated interests), however, this does not grow unbounded – in fact, it converges.

The Compound Interests (after a year) can be calculated as:

where:

is the total amount of money you will get, which includes pricipal P and compound interests earned.
is the principal balance aka the initial money deposited.
is the interest rate (AER).
is the number of interests applied over the period e.g. 1 year.

Translated to Python function:

1
2

def A(P, I, n):
  return P * (1 + I/n) ** n

def A(P, I, n):
  return P * (1 + I/n) ** n

When P=1, I=1 (100%), and n goes to infinity – the A approaches (has a limit of) the Euler’s number – e, the math constant which is roughly, (irrelational number).

–EOF (The Ultimate Computing & Technology Blog) —