## Sunday, October 21, 2012

### Interest

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? IA= PArT = 100 × 0.05 × 1 =5 AA= P A + I A = 100 + 5 =105 IC= PCrT = 105 × 0.05 × 1 =5.25 AC = 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?