Real-World Examples of Continuous Compound Interest in Finance

📚 Quick Study Guide

🧮 Continuous compound interest calculates interest constantly, not just annually or monthly. 📈 The formula for continuous compound interest is: $A = Pe^{rt}$, where:
• 🏦 $A$ = the future value of the investment/loan, including interest
• 💰 $P$ = the principal investment amount (the initial deposit or loan amount)
• ⏱️ $r$ = the annual interest rate (as a decimal)
• 📅 $t$ = the number of years the money is invested or borrowed for
• 📍 $e$ = Euler's number (approximately equal to 2.71828)
💡 Continuous compounding provides the highest possible return compared to other compounding frequencies.

🧪 Practice Quiz

1. What is the future value of a \$1,000 investment compounded continuously at an annual interest rate of 7% for 5 years?
   1. \$1,350.00
   2. \$1,419.07
   3. \$1,072.50
   4. \$1,500.00
2. Which of the following scenarios would result in the highest return on investment?
   1. Compounding annually at 8%
   2. Compounding quarterly at 8%
   3. Compounding monthly at 8%
   4. Compounding continuously at 8%
3. You invest \$5,000 in an account with continuous compounding. After 10 years, the investment is worth \$10,000. What is the annual interest rate?
   1. 5.93%
   2. 6.93%
   3. 7.93%
   4. 8.93%
4. What does 'P' represent in the continuous compound interest formula, $A = Pe^{rt}$?
   1. Annual interest
   2. Future value
   3. Principal investment
   4. Time in years
5. If you invest \$2,000 at a 6% annual interest rate compounded continuously, how long will it take for your investment to double?
   1. Approximately 9.5 years
   2. Approximately 10.5 years
   3. Approximately 11.5 years
   4. Approximately 12.5 years
6. What is the future value of \$3,000 invested for 3 years at 5% compounded continuously?
   1. \$3,477.11
   2. \$3,500.00
   3. \$3,050.00
   4. \$3,900.00
7. Which factor has the LEAST impact on the future value in continuous compounding?
   1. Principal investment amount
   2. Annual interest rate
   3. Number of years
   4. Daily stock market fluctuations