Espresso with Spoon for compound interest post

Compound interest is interest calculated on the principal and the accumulated interest. Simple interest by comparison is just calculated just based on the principal. Compound interest can be thought of as interest that build on top of interest.

When interest is working for you it’s like coasting down a hill with a strong tailwind. Paying back debt and working against the compound interest is like climbing uphill into a headwind. The magic of compound interest is the way that gains in interest build on themselves for further gains. This is great when it is working for you and a severe pain in the drain when it is working against you.

Uphill Credit Card Example

For an example of climbing up a hill into a blistering headwind of interest, lets look at a credit card. In this example I am assuming a staring balance of $1000.00. I’ll go with a middle of the road interest rate for a credit card of 25%. Further let’s assume that the intrepid hill climber only pays the 3% minimum each month. Lets see what this horror show looks like:

Month Principal Interest Total
1 30.00 20.83 50.83
2 29.10 20.21 49.31
3 28.23 19.60 47.83
4 27.38 19.01 46.39
5 26.56 18.44 45.00
6 25.76 17.89 43.65
7 24.99 17.35 42.34
8 24.24 16.83 41.07
9 23.51 16.33 39.84
10 22.81 15.84 38.65
11 22.12 15.36 37.49
12 21.46 14.90 36.36
13 20.82 14.46 35.27
14 20.19 14.02 34.21
15 19.59 13.60 33.19
16 19.00 13.19 32.19
17 18.43 12.80 31.22
18 17.87 12.41 30.29
19 17.34 12.04 29.38
20 16.82 11.68 28.50
21 16.31 11.33 27.64
22 15.82 10.99 26.81
23 15.35 10.66 26.01
24 14.89 10.34 25.23
25 14.44 10.03 24.47
26 14.01 9.73 23.74
27 13.59 9.44 23.03
28 13.18 9.15 22.33
29 12.79 8.88 21.66
30 12.40 8.61 21.01
31 12.03 8.35 20.38
32 11.67 8.10 19.77
33 11.32 7.86 19.18
34 10.98 7.62 18.60
35 10.65 7.40 18.05
36 10.33 7.17 17.50
37 10.02 6.96 16.98
38 9.72 6.75 16.47
39 9.43 6.55 15.98
40 9.15 6.35 15.50
41 8.87 6.16 15.03
42 9.02 5.98 15.00
43 9.21 5.79 15.00
44 9.40 5.60 15.00
45 9.60 5.40 15.00
46 9.80 5.20 15.00
47 10.00 5.00 15.00
48 10.21 4.79 15.00
49 10.43 4.57 15.00
50 10.64 4.36 15.00
51 10.86 4.14 15.00
52 11.09 3.91 15.00
53 11.32 3.68 15.00
54 11.56 3.44 15.00
55 11.80 3.20 15.00
56 12.04 2.96 15.00
57 12.30 2.70 15.00
58 12.55 2.45 15.00
59 12.81 2.19 15.00
60 13.08 1.92 15.00
61 13.35 1.65 15.00
62 13.63 1.37 15.00
63 13.91 1.09 15.00
64 14.20 0.80 15.00
65 14.50 0.50 15.00
66 9.50 0.20 9.70

66 months to pay back $1000.00 and it cost $578.11 in interest. That is not the sort of hill I like to climb. I went ahead and set a fixed payment on low balances of $15.00. That is why the payments leveled off at $15.00. Otherwise the repayment would have approached zero and taken a good while to get there. Lets try the same scenario but change it up a little by throwing an extra $50 a month on the payment:

Month Principal Interest Additional Total
1 80.00 20.83 50.00 100.83
2 77.60 19.17 50.00 96.77
3 75.27 17.55 50.00 92.82
4 73.01 15.98 50.00 89.00
5 70.82 14.46 50.00 85.28
6 68.70 12.99 50.00 81.68
7 66.64 11.55 50.00 78.19
8 64.64 10.17 50.00 74.80
9 62.70 8.82 50.00 71.52
10 60.82 7.51 50.00 68.33
11 58.99 6.25 50.00 65.24
12 57.22 5.02 50.00 62.24
13 55.51 3.82 50.00 59.33
14 53.84 2.67 50.00 56.51
15 52.23 1.55 50.00 53.77
16 22.00 0.46 21.34 22.46
17 0.00 0.00 0.00 0.00

Alright, that is much better. Throwing an extra $50.00 per month at the credit card reduced the number of payments from 66 to 17. More importantly the total interest paid dropped to $158.79. The takeaway here is that minimum payments as defined by the credit card companies is hogwash. The minimum payment is set low with the express intent of enriching the issuing company. Setting the minimum repayment percentage low allows compound interest to accrue as much as possible. The only reason to pay the minimum is because you’ve managed to get yourself in a bind and can only make the minimum payment while still feeding yourself.

Credit cards can be powerful tools when used well. By used well I mean paid in full every month before incurring interest charges. Don’t fret for the credit card company if you use the card this way. They still make money from the merchants you purchased from in the form of interchange fees. So they still make money even if you pay off the balance every month.

Downhill Example

Lets try a downhill with wind at our backs example with interest working for us. Let’s look at an investment that returns 2% annually and we will reinvest the earnings back into the fund. Two percent is a a bit below the current 10 year US treasury rate, so it is a pessimistically low assumption. I like throwing some padding into my assumptions. And this is for illustrative purposes anyway. I’ll start with no initial investment and save $2,000 a year.

Year Total
1 $2,000.00
2 $4,333.33
3 $7,055.56
4 $10,231.48
5 $13,936.73
6 $18,259.52
7 $23,302.77
8 $29,186.56
9 $36,050.99
10 $44,059.49

Over ten years the total amount invested was $20,000. With a steady return of 2% the final total is $44,059.49. That is some serious downhill compound interest magic.

Closing Thoughts

“The most powerful force in the universe is compound interest” – Apocryphal quote often attributed to Albert Einstein

That quote was the first thing I thought of when going to write this post. Unfortunately, I tend to check my sources and do a little digging before just posting stuff. And both Snopes and Stack Exchange are not entirely convinced Albert Einstein actually said that. It’s still a great quote, even if a famous physicist didn’t actually say it.

Getting paid interest in a good thing. Paying interest is bad.