90 Chapter 3 Compound Interest
With time, compound interest roars ahead, leaving simple interest in the dust. The compound
interest earned in the last year alone is almost as much as the total simple interest for the
entire 50 years! Clearly, compounding is a powerful force.A Formula for Compound Interest
Looking at things year by year is a good way to get a sense of how compound interest
works, but a tedious and impractical way of doing an actual calculation. Hopefully we can
find a more efficient way to calculate compound interest.
Let’s begin by noting that 8% interest for a single year on 1 dollar amounts to exactly
8 cents. Another way of saying this would be to note that in 1 year $1.00 turns into
$1.08. What happens to $5,000.00? Well, it stands to reason that a starting balanceSIMPLE INTEREST COMPOUND INTEREST
Year Start Interest End Start Interest EndDifference in
End Balance20 $12,600.00 $400.00 $13,000.00 $21,578.51 $1,726.28 $23,304.79 $10,304.79
21 $13,000.00 $400.00 $13,400.00 $23,304.79 $1,864.38 $25,169.17 $11,769.17
22 $13,400.00 $400.00 $13,800.00 $25,169.17 $2,013.53 $27,182.70 $13,382.70
23 $13,800.00 $400.00 $14,200.00 $27,182.70 $2,174.62 $29,357.32 $15,157.32
24 $14,200.00 $400.00 $14,600.00 $29,357.32 $2,348.59 $31,705.90 $17,105.90
25 $14,600.00 $400.00 $15,000.00 $31,705.90 $2,536.47 $34,242.38 $19,242.38
26 $15,000.00 $400.00 $15,400.00 $34,242.38 $2,739.39 $36,981.77 $21,581.77
27 $15,400.00 $400.00 $15,800.00 $36,981.77 $2,958.54 $39,940.31 $24,140.31
28 $15,800.00 $400.00 $16,200.00 $39,940.31 $3,195.22 $43,135.53 $26,935.53
29 $16,200.00 $400.00 $16,600.00 $43,135.53 $3,450.84 $46,586.37 $29,986.37
30 $16,600.00 $400.00 $17,000.00 $46,586.37 $3,726.91 $50,313.28 $33,313.28
31 $17,000.00 $400.00 $17,400.00 $50,313.28 $4,025.06 $54,338.35 $36,938.35
32 $17,400.00 $400.00 $17,800.00 $54,338.35 $4,347.07 $58,685.41 $40,885.41
33 $17,800.00 $400.00 $18,200.00 $58,685.41 $4,694.83 $63,380.25 $45,180.25
34 $18,200.00 $400.00 $18,600.00 $63,380.25 $5,070.42 $68,450.67 $49,850.67
35 $18,600.00 $400.00 $19,000.00 $68,450.67 $5,476.05 $73,926.72 $54,926.72
36 $19,000.00 $400.00 $19,400.00 $73,926.72 $5,914.14 $79,840.86 $60,440.86
37 $19,400.00 $400.00 $19,800.00 $79,840.86 $6,387.27 $86,228.13 $66,428.13
38 $19,800.00 $400.00 $20,200.00 $86,228.13 $6,898.25 $93,126.38 $72,926.38
39 $20,200.00 $400.00 $20,600.00 $93,126.38 $7,450.11 $100,576.49 $79,976.49
40 $20,600.00 $400.00 $21,000.00 $100,576.49 $8,046.12 $108,622.61 $87,622.61
41 $21,000.00 $400.00 $21,400.00 $108,622.61 $8,689.81 $117,312.42 $95,912.42
42 $21,400.00 $400.00 $21,800.00 $117,312.42 $9,384.99 $126,697.41 $104,897.41
43 $21,800.00 $400.00 $22,200.00 $126,697.41 $10,135.79 $136,833.20 $114,633.20
44 $22,200.00 $400.00 $22,600.00 $136,833.20 $10,946.66 $147,779.86 $125,179.86
45 $22,600.00 $400.00 $23,000.00 $147,779.86 $11,822.39 $159,602.25 $136,602.25
46 $23,000.00 $400.00 $23,400.00 $159,602.25 $12,768.18 $172,370.43 $148,970.43
47 $23,400.00 $400.00 $23,800.00 $172,370.43 $13,789.63 $186,160.06 $162,360.06
48 $23,800.00 $400.00 $24,200.00 $186,160.06 $14,892.80 $201,052.87 $176,852.87
49 $24,200.00 $400.00 $24,600.00 $201,052.87 $16,084.23 $217,137.09 $192,537.09
50 $24,600.00 $400.00 $25,000.00 $217,137.09 $17,370.97 $234,508.06 $209,508.06TABLE 3.1 Comparison of Simple and Compound Interest (Continued)