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 1.25971 1259.71 1.36049 1360.49 1.46933 1469.33 1.58687 1586.87 1.71382 1713.82 1.85093 1850.93 1.999 1999 2.15892 2158.92

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 1.5609 1560.9 1.81064 1810.64 2.10034 2100.34 2.4364 2436.4 2.82622 2826.22 3.27841 3278.41 3.80296 3802.96 4.41144 4411.44

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 1.08243 1082.43 1.17166 1171.66 1.26824 1268.24 1.37279 1372.79 1.48595 1485.95 1.60844 1608.44 1.74102 1741.02 1.88454 1884.54 2.03989 2039.89 2.20804 2208.04

 1000 1.04 1.16986 1169.86 1.36857 1368.57 1.60103 1601.03 1.87298 1872.98 2.19112 2191.12 2.5633 2563.3 2.9987 2998.7 3.50806 3508.06 4.10393 4103.93 4.80102 4801.02

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.