3-6 Continuous Compounding Answer Key

3-6 Continuous Compounding Answer Key provides a comprehensive solution guide for continuous compounding problems. This resource offers step-by-step explanations and answers to help learners understand and master the concept of continuous compounding. By using this answer key, students can practice and check their work to ensure accuracy and improve their skills in financial mathematics. Watch the video below to see a demonstration of how to use the answer key effectively.

Answer Key for 3-6 Continuous Compounding

Continuous compounding is a powerful concept in finance that allows for the calculation of interest on an investment or loan that is constantly compounded. In this scenario, the interest earned or charged is added to the principal continuously, leading to exponential growth or decay of the investment or debt. In this article, we will provide the answer key for problems related to 3-6 continuous compounding.

Let's start with a basic formula for continuous compounding:

\[ A = P \times e^{rt} \]

Where:

• A is the future value of the investment or debt
• P is the principal amount (initial investment or loan amount)
• e is the base of the natural logarithm (approximately equal to 2.71828)
• r is the annual interest rate
• t is the time the money is invested or loaned for, in years

Now, let's work on some problems related to continuous compounding:

Problem 1: If you invest $1000 at an annual interest rate of 5% for 3 years with continuous compounding, what will be the future value of your investment?

Solution 1: Using the formula A = P * e^(rt), we can plug in the values:

\[ A = 1000 \times e^{0.05 \times 3} \]

Calculating this, we get:

\[ A = 1000 \times e^{0.15} \approx 1000 \times 1.16183 \approx 1161.83 \]

Therefore, the future value of your investment after 3 years with continuous compounding will be approximately $1161.83.

Problem 2: If you borrow $5000 at an annual interest rate of 8% for 6 years with continuous compounding, how much will you owe at the end of the loan term?

Solution 2: Using the same formula A = P * e^(rt), we can substitute the given values:

\[ A = 5000 \times e^{0.08 \times 6} \]

Calculating this, we get:

\[ A = 5000 \times e^{0.48} \approx 5000 \times 1.61818 \approx 8090.91 \]

Therefore, at the end of the 6-year loan term with continuous compounding, you will owe approximately $8090.91.

This concludes the answer key for problems related to 3-6 continuous compounding. Continuous compounding is a fundamental concept in finance that allows for precise calculations of interest over time, taking into account the compounding effect. Understanding how to apply the formula and solve problems related to continuous compounding is essential for financial analysis and decision-making.