Calculus Intelligence Agency

34564 Astuteness Boulevard

Mystery City, Enigma 34564

Dr. I.R. Service

The White House

1600 Pennsylvania Avenue NW

Washington, DC 20500

Dear Dr. I.R. Service:

If the President’s staff selects you, you will definitely face a stiff set of confirmation hearings in front of the U.S. Senate. The C.I.A. (Calculus Intelligence Agency) is here to help you become more intellectually stimulated by our findings. Our findings report whether or not the reported receipts and outlays for various years actually yield values for the national debt that are close to the reported values. The following information and data will prove that the C.I.A. has done an accurate investigation.

To investigate the allegations that a member of Ross Perot’s political party has made regarding the federal debt, we began with the summarized data given to you in table form. To ease calculations, we used 0 for year 1939 and 52 for year 1991. This made it much simpler to find the formula for a curve that approximates the data. The formula for that curve is:

Y = -0.2596x4 + 31.51x3 – 1030.8x2 + 8938.4x + 18965

with Y being the deficit in millions, and x being the number of years after 1939.

Left sum

Right sum

15448 / 229684
57421 / 51423
51423 / 53941
269705 / 15610
18732 / -24522
-16348 / -1076
-1345 / 7985
7985 / 14225
14225 / 225540
225540 / 294805
294805 / 1014065
202813 / 220698
220698 / 148004
148004 / 155102
155102 / 151952
151952 / 220388
220388 / 268729
Total: / Total:
2036548 / 3046553

The area under the curve should closely approximate the national debt, since the Y-axis is dollars per year, and X-axis is years. To find the area under this curve, we used all five of the methods that Professor Cox had taught us. To find the range of answers that we should get, we found the left and right sum. To get these numbers, we multiplied the interval (that is, the change in x between two consecutive years) by a dollar value given in the table. For the left sum, we multiplied it by the dollar value of the left year—the one with the lower x-value. For the right sum, we multiplied it by the right year, which is the one with the higher value.

Trapezoid sum
122566
54422
52682
142657.5
-2889.3*
-8712
3321.18*
11105
119882.5
260172.5
654435
211755.5
184351
151553
153527
186170
244558.5
Total:
2541557.38

The Trapezoid sum was next. We used the area formula:

½ (B1+B2)*H

to find the area of each trapezoidal section, with B1 and B2 being the years, and H being the interval. There were two intervals, however, that were not trapezoids. These were the years where the deficit changed from positive to negative, or from negative to positive, and are marked with asterisks. These intervals were actually two triangles, which we found the area of separately and added together.

For our midline sum, we needed to use our curve formula. We divided the curve into 26 slices, each slice with an interval of 2, and found the y-coordinates of the midpoint of each slice. The data is given on the next page.

Midpoint Sum
Midpoint / Y-value / Slice Area
1 / 27075.354 / 54150.708
3 / 37148.326 / 74296.651
5 / 41314.563 / 82629.126
7 / 40846.283 / 81692.566
9 / 36919.614 / 73839.229
11 / 30614.594 / 61229.189
13 / 22915.171 / 45830.341
15 / 14709.201 / 29418.402
17 / 6788.454 / 13576.908
19 / -151.39303 / -302.78606
21 / -5510.7518 / -11021.504
23 / -8786.1242 / -17572.248
25 / -9570.1022 / -19140.204
27 / -7551.3675 / -15102.735
29 / -2514.6918 / -5029.3836
31 / 5659.0631 / 11318.126
33 / 16992.946 / 33985.891
35 / 31413.914 / 62827.829
37 / 48752.838 / 97505.675
39 / 68744.494 / 137488.99
41 / 91027.572 / 182055.14
43 / 115144.67 / 230289.34
45 / 140542.3 / 281084.6
47 / 166570.87 / 333141.75
49 / 192484.73 / 384969.45
51 / 217442.09 / 434884.19
Total: / 2638045.2

The C.I.A. plugged in the actual deficit for years 1939 through 1991 into the formula above. The actual deficit was determined by subtracting the outlay from the revenue for each given year. The C.I.A. utilized five calculus methods to estimate the national debt. The C.I.A. estimates the national debt to be $2,036,548 million with the left sum estimation method. The C.I.A. estimates the national debt to be $3,046,553 million with the right sum estimation method. The C.I.A. utilized the trapezoid sum, which estimated the national debt to be $2,541,557 million. The midline sum was estimated by the C.I.A. to give the national debt to be $2,638,045 million. The C.I.A. determined the national debt approximated by the Integral of the Quarctic formula. The formula is given above. The approximate national debt since 1939 was $2,638,577 million. Our approximate total national debt in 1991 was $2,678,577 million.

The Treasury Department, in 1939, claimed the national debt was $40 billion. The Ross Perot’s political party has made the claim that the debt had risen to $3,665 billion in 1991. The data given by the C.I.A. verifies that there is evidence against a significant discrepancy between the national debt and the accumulation of reported deficits.

We are proud to be Americans!

Calculus Intelligence Agency

aka C.I.A

Agents Martin Sector, Samirah Abdelfattah, and Willie Leach