Simple Versus Compound Interest Fundamentals - Part I
1. Simple versus Compound Interest: The Fundamentals
1. Why interest type matters
Interest is the rental fee you pay to use someone else’s money or the reward you earn for letting someone else use yours. The two most common ways to compute that fee are simple interest and compound interest. Simple interest is calculated only on the original principal, so the charge added each period never changes.
It appears in many auto loans and short-term installment loans because the math is straightforward and the payment schedule is easy to explain [1]. Compound interest, by contrast, treats previously accrued interest as fresh principal, so every period the base grows and the calculation is repeated on a slightly larger sum. Savings accounts, certificates of deposit, and most credit-card balances use this method [2].
Over long horizons, the difference between the two methods widens dramatically because compounding follows an exponential curve while simple interest grows in a straight line. Understanding which method applies to your debt or investment is therefore one of the most powerful pieces of financial literacy you can acquire early in life.
2. Formulas, numbers, and real-world impact
You can see the mechanics in the formulas.
- Simple interest: I = P × r × t
- Compound interest: A = P (1 + r / n)^(n t)
In each formula, P is the original principal, r is the annual rate expressed as a decimal, n is the number of compounding periods per year, and t is time in years [3].
Imagine investing $1,000 at 5 percent for ten years. Under simple interest the balance reaches $1,500, but annual compounding delivers about $1,628.89—an extra $128.89 without adding a cent of new money [4].
A quick mental shortcut for compound growth is the Rule of 72: divide 72 by the interest rate to estimate doubling time, so at 6 percent funds double in roughly twelve years [5]. The same arithmetic turns against borrowers: an 18 percent credit-card balance doubles in just four years if unpaid.
1. Did Einstein really say that?
The oft-quoted line “Compound interest is the eighth wonder of the world” is widely attributed to Albert Einstein, yet historians can find no record of him uttering it. The earliest known appearance was actually in a 1925 New York savings-bank advertisement—not in a physics lecture .
2. Rule of 72 in your pocket
Divide 72 by any interest rate to approximate how long it takes money—or debt—to double. At 9 percent, it is about eight years; at 3 percent, roughly twenty-four. The trick works because 72 is close to the natural logarithm base used in compound-growth math.
2. Reading amortization schedules line by line
1. Amortization schedules basics
Amortization schedules turn the abstract promise of “thirty years of payments” into a month-by-month ledger that shows where every dollar of a loan payment is going.
Each row lists the period, beginning balance, required payment, interest portion, principal portion, and the new ending balance, creating a transparent timeline from the first check to the loan’s payoff date.[6] Because interest is computed on the outstanding balance, early payments are interest-heavy: on a typical fixed-rate mortgage, more than 60 % of the first year’s outflow services interest rather than principal.[7] As the balance shrinks, the interest charge falls and an ever-larger slice of the same level payment attacks principal.
Seeing this shift on paper (or in Excel) helps mid-career professionals forecast equity growth, evaluate refinancing offers, or estimate the impact of an extra $100 paid toward principal each month. Many lenders supply downloadable schedules, but free spreadsheet templates let you tweak rate changes, biweekly payments, or lump-sum prepayments to test “what-if” scenarios with a few keystrokes.[8]
1. Shortcut to interest savings
Making one additional principal-only payment equal to a single month each year on a 30-year fixed mortgage typically chops 4–5 years off the term and can save tens of thousands of dollars in interest—without refinancing or changing the required payment schedule.
References
- [1] CFPB explanations of loan basics
- [2] Federal Reserve education materials
- [3] Simple vs. Compound Interest Formulas
- [4] SEC compound interest calculator
- [5] Rule of 72
- [6] Investopedia: What Is an Amortization Schedule?
- [7] Investopedia: Why Is Most of My Payment Going to Interest?
- [8] Business Insider: Mortgage Amortization Schedules Explained