Name



Name : ________________________

Compound/Continuous Interest

Complete the table for a savings account subject to n compoundings yearly[pic].

| |Principal |Number of Compoundings |Annual Interest Rate |Accumulated Amount |Time t in Years |

|1 |$1250 |4 |5.75% | |13 |

|2 |$7250 |12 |6.5% |$15000 | |

Complete the table for a savings account subject to continuous compounding[pic].

| |Principal |Annual Interest Rate |Accumulated Amount |Time t in Years |

|3 |$2350 |8% |Triple the amount invested | |

|4 |$8000 |2.35% | |10 |

[pic]

How long would it take a $2000 deposit to triple, if invested at a 7.5 % rate and compounded quarterly?

What principal should be deposited at 6.35 % compounded daily to ensure the account will be worth $15,000 in 20 years?

The CONTINUOUS Growth of the World

1) According to the CIA World Fact Book, The Commonwealth of the Northern Mariana Islands is experiencing a decrease in population at a continuous rate of 7.08% each year. (It consists of 15 islands about three-quarters of the way from Hawaii to the Philippines and is a commonwealth in political union with the United States in case you wondered. It also has the highest female to male ration in the world with 1.3 women per man!!!!)

As of 2005, The Northern Mariana Islands has a population of 80,362. Assuming that the population continues to decrease,

a) What is the population of the CNMI in 2011?

b) In what year will population reach 10,000?

2) The country with the highest growth rate is Burundi. The average woman in Burundi will have 6 children. In 2008, it is estimated that the country 8.7 million residents. Assume that the current growth rate of 3.69% continues and that this growth is continuous. It is located in Africa right next to Rwanda in case you want to go looking for it.

a) What will be the population of Burundi in the year 2013?

b) It what year will the population have doubled? (aka 17.4 million)

3) It is reported that Austria has a continuous growth rate of 0.05%. The population is estimated to be 8.4 million as of 2009. Assuming this growth rates continues, what will be the population of Austria in the year 3000? (Notice that your answer isn’t even twice the current population!)

4) In Mexico, the growth rate is estimated at 1.13%. The population in 2010 is estimated to be 112 million. If the growth rate remains constant and is considered to be continuous, when will Mexico’s population be 130 million?

5) The country with the highest population in the world in China. The population of China is estimated to be 1.34 billion as of this morning. The growth rate is around 0.47% and is continuous. In what year will the population reach 2 billion?

6) Qatar is considered to be the richest country in the world with a per capita income of $81,963. For comparison, the per capita income in the US is $47,701. The country is just north of Saudi Arabia in case you want to make travel plans. According to a 2010 census, the population of Qatar is 1,696,563 and there is a continuous growth rate of 0.96%.

a) What will be the population of Qatar in the year 2060?

b) When will the population reach 3 million?

7) One of the poorest countries in the world also has one of the highest fertility rates in the world. The country of Niger has a per capita income of $719 and the average woman will give birth to 8 babies during her lifetime. Because of this birthrate, Niger comes in 2nd in growth with a continuous growth rate of 3.68%. In 2009, the population was estimated at 15.3 million. When will Niger have a population of 45 million?

8) Latvia has a population that is decreasing at a continuous rate of 0.61%. If the current population is 2.2 million, when will the population reach 1.5 million?

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