Johnny, Mary, and Ifran each have $100. There are only
two banks in town. However, they both offer 5% simple interest.

Johnny puts his money in Ambank for 2 years. Here is
what he gets:

I = PrT

= 100 × 0.05 × 2

= 10

A = P + I

= 100 + 10

=110.

How much would does Mary get if she puts her money in CIMB
Bank for 2 years? Obviously, the same amount.

Irfan decides to put his money in Ambank for the first
year; then withdrew everything from Ambank and put it in CIMB Bank for the
second year. What does he get?

I

_{A}= P_{A}rT
= 100 × 0.05 × 1

=5

A

_{A}= P_{ A}+ I_{ A}
= 100 + 5

=105

I

_{C}= P_{C}rT
= 105 × 0.05 × 1

=5.25

A

_{C }= P_{ C}+ I_{ C}
= 105 + 5.25

=110.25

Irfan has made a bigger profit than Johnny and Mary
have.

Question: Where did the extra 25 cents come from?

Answer: Compound Interest.

When Johnny kept his money with Ambank for

__2 years at simple interest__he did not get any benefit from the interest earned in the first year. That is, he was earning interest on $100 in year 1 and he were still earning interest on the same $100 in year 2. Likewise, for Mary’s money at CIMB. But when Irfan took his money out of Ambank, he started earning interest on $105 in year 2. In other words, in year 2, he was earning interest on the principal and*interest on the first year’s interest*. Hence ‘compound’ interest.
Now banks don’t want people rushing around at the end
of the year withdrawing and depositing money.
Half of the town would take money from bank A and put it in Bank B. The
other half would take money out of Bank B and put it in Bank A. Hence, each
bank will decide to credit the customer’s account

__at the end of the year__and let him or her earn interest on the principal and interest on the interest.
Is that the end of the story? Not necessarily, suppose
a new bank opens up in town and offers monthly interest. Responding to that threat, another bank
offers weekly interest. Where will it stop?

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