This assignment dealt with working with a spreadsheet. I decided to do some growth problems involving savings and compound interest. Here are the results of putting in $1000 and saving it at 8% interest compunded yearly. In just over nine years you will double your money as the data shows:

1000 | 1.08 | 1.08 | 1080 |

1.1664 | 1166.4 | ||

1.259712 | 1259.712 | ||

1.36048896 | 1360.48896 | ||

1.4693280768 | 1469.3280768 | ||

1.586874322944 | 1586.874322944 | ||

1.71382426877952 | 1713.82426877952 | ||

1.85093021028188 | 1850.93021028188 | ||

1.99900462710443 | 1999.00462710443 | ||

2.15892499727279 | 2158.92499727279 |

Now let's look at what happens when the same amount is saved at 16% interest, it would seem that the amount should double in just under 5 years, let's see if the results show this:

1000 | 1.16 | 1.16 | 1160 |

1.3456 | 1345.6 | ||

1.560896 | 1560.896 | ||

1.81063936 | 1810.63936 | ||

2.1003416576 | 2100.3416576 | ||

2.436396322816 | 2436.396322816 | ||

2.82621973446656 | 2826.21973446656 | ||

3.27841489198121 | 3278.41489198121 | ||

3.8029612746982 | 3802.9612746982 | ||

4.41143507864991 | 4411.43507864991 |

The data seems to support our hypothesis. Now let's look at what happens when the interest is compounded quarterly instead of annually. The next two tables show the same amount being saved at the same two interest rates except the interest will be compunded quarterly instead of annually:

1000 | 1.02 | 1.08243216 | 1082.43216 |

1.17165938100227 | 1171.65938100227 | ||

1.26824179456255 | 1268.24179456255 | ||

1.37278570509061 | 1372.78570509061 | ||

1.48594739597835 | 1485.94739597835 | ||

1.60843724947523 | 1608.43724947523 | ||

1.74102420617393 | 1741.02420617393 | ||

1.88454059210113 | 1884.54059210113 | ||

2.0398873437157 | 2039.8873437157 | ||

2.20803966361485 | 2208.03966361485 |

1000 | 1.04 | 1.16985856 | 1169.85856 |

1.36856905040527 | 1368.56905040527 | ||

1.60103221856768 | 1601.03221856768 | ||

1.87298124572719 | 1872.98124572719 | ||

2.19112314303342 | 2191.12314303342 | ||

2.56330416489175 | 2563.30416489175 | ||

2.99870331918227 | 2998.70331918227 | ||

3.50805874684579 | 3508.05874684579 | ||

4.10393255398042 | 4103.93255398042 | ||

4.80102062793666 | 4801.02062793666 |

As we would expect compunding quarterly does increase our amount a little more than compounding annually but not as much as one might think as the doubling theory shows, looking at tables 3 and 4, the oridinal amount doubles around the same time it doubled when compunding annually, which makes one think that compounding quarterly has more effect as the number of years grows large.