Interest Rates and Compounding
An interest rate is the "price of money". Compounding makes time your most powerful force, and central banks influence everything through the policy rate.
Key takeaways
- 1Simple interest is paid only on the principal; compound interest earns "interest on interest", and the gap widens over time.
- 2At the same annual rate, more frequent compounding gives a slightly higher effective annual return.
- 3Rule of 72: 72 ÷ annual rate (%) ≈ the number of years it takes to double your money.
- 4The central bank's policy rate affects borrowing costs, which in turn affect bonds, stocks and exchange rates.
Check your understanding
Get every question right to complete this lesson
1.You deposit $1,000 at 10% compounded annually for 2 years. Roughly what do you have at the end?
2.When the central bank raises rates, loan rates usually…
3.At 8% compounded annually, roughly how many years does it take to double your money?
Text version · Interest Rates & Swaps, lesson 1: “Interest Rates and Compounding”
An interest rate is the "price of money". Compounding makes time your most powerful force, and central banks influence everything through the policy rate.
Compound interest: interest earns interest too
An interest rate is “the price of money”. Simple interest is only paid on the principal; compound interest adds the interest to the principal, so next year interest is paid on the interest too, and the purple segment keeps growing.
The policy rate: the anchor for every rate
When the central bank changes the policy rate, banks' deposit and lending rates follow, which in turn affects mortgages, business funding, bonds and exchange rates.
Rule of 72: how long to double
Divide 72 by the annual rate (%) to estimate how many years compound interest takes to double your money: about 9 years at 8%, about 18 at 4%. Flip it around: with 3% inflation, prices double in about 24 years.
Key takeaways
- Simple interest is paid only on the principal; compound interest earns "interest on interest", and the gap widens over time.
- At the same annual rate, more frequent compounding gives a slightly higher effective annual return.
- Rule of 72: 72 ÷ annual rate (%) ≈ the number of years it takes to double your money.
- The central bank's policy rate affects borrowing costs, which in turn affect bonds, stocks and exchange rates.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Click “Example: $1,000 × 10% × 2 years”: what's the amount at maturity? How many dollars of it are “interest on interest”?
- Set the years to 30 and press ▶: when does the purple “interest on interest” overtake the orange regular interest?
- Keep 10% and switch the compounding frequency from “Yearly” to “Monthly” to “Daily”: what does the “Effective annual rate” card show each time?
- Click “Hike 0.25%” three times: how much more is the monthly payment on a $300,000 mortgage? Then try cutting back.
Quiz and explanations
- 1. You deposit $1,000 at 10% compounded annually for 2 years. Roughly what do you have at the end?
- Answer: $1,210.$1,000 × 1.1 × 1.1 = $1,210.
- 2. When the central bank raises rates, loan rates usually…
- Answer: Rise.The policy rate is the anchor for borrowing costs.
- 3. At 8% compounded annually, roughly how many years does it take to double your money?
- Answer: 9 years.72 ÷ 8 = 9 years (the exact figure is about 9.01 years).
Terms in this lesson
- compound interest (Compound Interest): Interest that earns interest of its own, so your money snowballs.
- interest rate (Interest Rate): The price of borrowing money, usually shown as an annual percentage.
- policy rate (Policy Rate): The benchmark rate set by a central bank, which drives borrowing costs across the economy.