Assignment #12

by

Jim Meneguzzo


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.