Compound interest introduction | Interest and debt | Finance & Capital Markets | Khan Academy

TL;DR

Learn about compounding interest and how to approximate the time it takes to double your money using the Rule of 72.

Transcript

Male Voice: What I want to do in this video is talk a little bit about compounding interest and then have a little bit of a discussion of a way to quickly, kind of an approximate way, to figure out how quickly something compounds. Then we'll actually see how good of an approximation this really is. Just as a review, let's say I'm running some type ... Read More

Key Insights

• 👻 Compounding interest allows investments to grow faster by earning interest on interest.
• ✖️ The formula to calculate the value of an investment after n years is the principal multiplied by (1 + interest rate)^n.
• ☠️ The Rule of 72 is a simple method to estimate the time it takes for an investment to double and involves dividing 72 by the interest rate.
• ☠️ The Rule of 72 provides a reasonably accurate approximation for interest rates between 6% and 10%.
• 😒 Calculating compounding interest precisely can be complex and may require the use of logarithms.
• 🔨 The Rule of 72 is a useful tool for quickly understanding the impact of compounding interest without complex calculations.
• ☠️ The Rule of 72 becomes less accurate for interest rates outside the range of 6% to 10%.

Questions & Answers

Q: What is compounding interest?

Compounding interest is when the interest earned on an initial deposit is reinvested, resulting in earning interest on interest over time. It allows investments to grow faster.

Q: How is compounding interest calculated?

To calculate compounding interest, multiply the principal amount by one plus the interest rate raised to the power of the number of compounding periods. This formula accounts for growth due to interest over time.

Q: What is the Rule of 72?

The Rule of 72 is a quick estimate to determine how long it takes for an investment to double in value. Divide 72 by the interest rate to get a rough approximation of the number of years it takes to double.

Q: How accurate is the Rule of 72?

The Rule of 72 provides a relatively accurate estimation for compounding interest, especially for interest rates between 6% and 10%. The approximation becomes less precise as interest rates deviate further from this range.

Summary & Key Takeaways

• Compounding interest occurs when the interest earned on an initial deposit is added to the deposit, resulting in increasing interest with each compounding period.

• The formula to calculate the value of an investment after n years is the principle multiplied by (1 + interest rate)^n.

• The Rule of 72 is an approximate method to determine the time it takes for an investment to double in value, where 72 is divided by the interest rate to get the rough estimation of years.