Evil Interest

Everybody with a savings account or almost any form of debt has at least a passing familiarity with interest.   How many of you actually know what it is, or even how much you are actually paying?

 

First, some definitions.

Principal is the term used for the amount of money you have borrowed.

Interest is the rent you pay to have that money.   Interest is money-rent, expressed as a percentage of the principal.  If you borrow $100 at 10%, you pay approximately $10 in interest.   I say “approximately” because it’s just not that simple.

There are two kinds of interest: simple and compound.

Simple interest is called that because it is just that: simple.   It’s easy to understand and it’s what most people mistakenly assume they are paying.  With simple interest, the interest rate is only applied to the principal, never to the accumulated, or accrued, interest.

For example, if you have borrowed $100 at 10% annual interest, this is what your balance will look like:

• At the time of borrowing the money, you owe $100.
• After 1 year, you owe 10% of the $100, in addition to the original $100: $110.
• After 2 years, you owe 10% of the $100, in addition to the original $100 and year one’s interest: $120.
• After 10 years, you will owe a total of $200.

That’s simple.

On the other hand, in addition to five more fingers, you have compound interest.   Compound interest complicates things considerably. With compound interest, interest is applied to the entire balance of what you owe; both the principal and the accrued interest are included in the calculation.

For example, with $100 at 10% compounded annually:

• Year 1: You will owe $100 + 10% of the original $100, or $110
• Year 2: You will owe $110 + 10% of the $110, or $121
• Year 3: You will owe $121 + 10% of the $110, or $133.10
• Year 4: You will owe $131.10 + 10% of the $110, or $144.41
• Year 5: You will owe $144.41 + 10% of the $110, or $158.85
• Year 6: You will owe $158.85+ 10% of the $110, or $174.74
• Year 7: You will owe $174.74 + 10% of the $110, or $192.21
• Year 8: You will owe $192.21 + 10% of the $110, or $211.43
• Year 9: You will owe $211.43 + 10% of the $110, or $232.57
• Year 10: You will owe $232.57 + 10% of the $110, or $255.83

That is a total of $155.83 in interest paid over 10 years, or $15.58 per year, for an effective interest rate of 15.583%.

To throw another twist into the mix, interest is rarely compounded annually.  Monthly, or even daily, is much more common.   With monthly compounded interest, the annual rate, or APR, is divided by 12 and recalculated every month.

For example, using the same $100 at 10% APR, compounded monthly:

Since the interest rate is compounded monthly, we will be using the monthly periodic rate, which is 10% / 12, or .83%

• Month 1: $100 + .83% of $100 = $100.83
• Month 2: $100.83 + .83%  = $101.67
• Month 3: $101.67 + .83% = $102.51
• Month 4: $102.51 + .83% = $103.36
• Month 5: $103.36 + .83% = $104.22
• Month 6: $104.22 + .83% = $105.08
• Month 7: $105.08 + .83% = $105.95
• Month 8: $105.95 + .83% = $106.83
• Month 9: $106.83 + .83% = $107.72
• Month 10: $107.72 + .83% = $108.61
• Month 11: $108.61 + .83% = $109.51
• Month 12: $109.51 + .83% = $110.42

That’s $0.42 more interest paid the first year, and that number will continue to climb each year the interest is compounded.

It gets worse if interest is compounded daily, like most credit cards.   If you see “Daily Periodic Rate” anywhere in your agreement, you are getting compounded daily.   This same loan, compounded daily instead of monthly will yield $110.51 owed the first year.   That $0.51 might not seem like much, but imagine it on a $10,000 credit card, or a $100,000 house!  And that’s just the first year.   Every year after, the disparity gets bigger.

Edit: The formula for calculating compounding interest is Principal x (1 + rate as a decimal / compounding term)^{compounding term}. So, for $100 at 10% compounded monthly, the formula is 100 x (1 + 0.1 / 12)¹²

That’s the downside to compounding interest. There is an upside, if you have investments or interest-bearing accounts.   If that’s the case, compounding interest is working in your favor.

If you save $100 per week, and manage to get a 10% return on your investment, you will have $331,911 after 20 years(with $104,000 contributed)  and $2,784,424 after 40(with $208,000 contributed).   That mean you will have tripled your money in 20 years, or vingtupled* it in 40 years.

That’s how you get rich. $100 per week for the rest of your life will leave you with a comfortable retirement, without missing out on life now.

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* Yes, it’s a real word**.  It means a twenty-fold increase.

** No, I did not know that yesterday.