Answer to September 10, 2001 ProblemContributed by Keith Mealy |
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| Compound Interest Problem |
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Two twins, Benjamin and Albert, graduate from high
school at age 18. Ben, an industrious type, works an
extra job delivering pizza and puts $2000 on the first of
each year into an IRA. Al, meanwhile, works on his
Ph.D. and spends his meager stipend on Pizza and Root Beer
at State U. Ten years later, Ben is busy running his
print shop, has a family and decides he can't
contribute to his IRA any more, so he stops contributing.
Meanwhile, Al at 28, has graduated, and has landed a
new teaching job and starts putting his $2000 a year
into his new IRA.
Forty years later at the age of 68, both are ready to retire. Ben has
contributed $20,000 to his IRA (during the first ten years). Al has contributed
$80,000 to his IRA (during the last forty years), four times as much.
Assuming both Ben and Al earn 8% every year compounded annually
(figured on the last day of the year),
how much does each have for their retirement?
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Solution to Problem: Ben has $679,781.46 and Al has $559,562.08 Further, even if Al continues to add $2000 a year to his IRA, he will never catch up to Ben. The extra $120,000 earns $9600 in the next year, and more each year, thanks to compounding.
Change the problem to 11.5%, the historical average
stock market return, and the numbers are:
Below is a computer printout showing the balance for each year:
Ben's Ben's Albert's Albert's
Year Deposits Balance Deposits Balance
---- -------- --------- ------- ----------
1 2000.00 2160.00 0.00 0.00
2 2000.00 4492.80 0.00 0.00
3 2000.00 7012.22 0.00 0.00
4 2000.00 9733.20 0.00 0.00
5 2000.00 12671.86 0.00 0.00
6 2000.00 15845.61 0.00 0.00
7 2000.00 19273.26 0.00 0.00
8 2000.00 22975.12 0.00 0.00
9 2000.00 26973.12 0.00 0.00
10 2000.00 31290.97 0.00 0.00
11 0.00 33794.25 2000.00 2160.00
12 0.00 36497.79 2000.00 4492.80
13 0.00 39417.62 2000.00 7012.22
14 0.00 42571.03 2000.00 9733.20
15 0.00 45976.71 2000.00 12671.86
16 0.00 49654.84 2000.00 15845.61
17 0.00 53627.23 2000.00 19273.26
18 0.00 57917.41 2000.00 22975.12
19 0.00 62550.80 2000.00 26973.12
20 0.00 67554.87 2000.00 31290.97
21 0.00 72959.26 2000.00 35954.25
22 0.00 78796.00 2000.00 40990.59
23 0.00 85099.68 2000.00 46429.84
24 0.00 91907.65 2000.00 52304.23
25 0.00 99260.26 2000.00 58648.57
26 0.00 107201.09 2000.00 65500.45
27 0.00 115777.17 2000.00 72900.49
28 0.00 125039.35 2000.00 80892.53
29 0.00 135042.49 2000.00 89523.93
30 0.00 145845.89 2000.00 98845.84
31 0.00 157513.56 2000.00 108913.51
32 0.00 170114.65 2000.00 119786.59
33 0.00 183723.82 2000.00 131529.52
34 0.00 198421.73 2000.00 144211.88
35 0.00 214295.47 2000.00 157908.83
36 0.00 231439.10 2000.00 172701.54
37 0.00 249954.23 2000.00 188677.66
38 0.00 269950.57 2000.00 205931.87
39 0.00 291546.62 2000.00 224566.42
40 0.00 314870.34 2000.00 244691.74
41 0.00 340059.97 2000.00 266427.07
42 0.00 367264.77 2000.00 289901.24
43 0.00 396645.95 2000.00 315253.34
44 0.00 428377.63 2000.00 342633.61
45 0.00 462647.84 2000.00 372204.30
46 0.00 499659.66 2000.00 404140.64
47 0.00 539632.44 2000.00 438631.89
48 0.00 582803.03 2000.00 475882.44
49 0.00 629427.28 2000.00 516113.04
50 0.00 679781.46 2000.00 559562.08
Click here to see the C++ Program which generated the data above |
| 1. Matt Crandell | Winchester, Virginia |
| 2. Richard K. Johnson | La Jolla, California |
| 3.John Funk | Ventura, California |
| 4. Walt Arrison | Philadelphia, Pennsylvania |
| 5. Joe Heintz | Manchester, Tennessee |
| 6. Izzy Kushnir | Closter, New Jersey |
| 7. Janine Oliver | Winchester, Virginia |
| 8. Dave Denison | Fisher's Island, New York |
| 9. Renata Sommerville | Austin, Texas |
| 10. Tori Eads | Winchester, Virginia |