Continuous Interest/ Interest in Daily Basis(Finding for the Principal, Future Value, and Time)

Summary

In this educational video, the instructor discusses the concept of continuous interest, illustrating its application in real-life scenarios like investments and population growth. Through multiple examples, viewers learn how to calculate future investment values using the Euler's constant and logarithmic functions. The instructor walks through various scenarios, showing how to determine future values, initial investments, and time required to reach certain amounts. The video encourages students to engage with the material by pausing and trying calculations independently, making complex financial concepts accessible and relatable.

Takeaways

• 😀 Continuous interest refers to interest that is calculated on a daily basis, as seen in various applications like population growth and investments.
• 💰 The formula for calculating future value (F) with continuous compounding is F = P * e^(rt), where P is the principal, r is the rate, and t is the time.
• 📈 Example 1: Jas Meine invests $2,658 at a 9% interest rate for 15 years, leading to a future value of approximately $10,253.
• 📊 Example 2: Maria invests $6,154 at an 8% interest rate for 10 years, resulting in a future value of approximately $13,695.
• 💡 The formula can be rearranged to find the initial investment (P) given the future value (F), rate (r), and time (t).
• 🧮 Example 3: Anali's future value is $14,371.6 after 20 years at a 6.79% rate. The initial investment is calculated to be approximately $3,610.
• 📉 Example 4: John’s investment grows to $1,912.41 after 15 years at a 0.63% rate, requiring an initial investment of approximately $1,289.
• 🕒 Example 5: Elma’s investment of $8,589 at a 7% rate is projected to grow to $21,337.85 in about 13 years.
• 🔍 Logarithms can be utilized to solve for the time or rate when calculating continuous compounding investments.
• 💬 Viewers are encouraged to ask questions in the comments and to like and subscribe for more helpful content.

Q & A

What is continuous interest?

Continuous interest refers to interest that is calculated and added to the principal balance at every possible instant, rather than at discrete intervals, leading to exponential growth of the investment.

What is the formula for calculating future value with continuous compounding?

The formula is F = P * e^(rt), where F is the future value, P is the principal amount, r is the annual interest rate, t is the time in years, and e is Euler's constant (approximately 2.71828).

How is Euler's constant used in the context of investments?

Euler's constant is used in the formula for continuous compounding to model how money grows over time with interest applied continuously.

How do you calculate the future value of an investment?

To calculate the future value, substitute the principal amount, the interest rate, and the time into the formula F = P * e^(rt).

What was Jas's account balance after 15 years with a principal of $2,658 at 9% interest?

Jas's account balance after 15 years was approximately $10,253.40.

What process was used to find the principal amount for Anali's future value of $14,371.60?

To find the principal amount, we rearranged the formula to P = F / e^(rt) and calculated using the given future value, rate, and time.

What is the significance of compounding frequency in interest calculations?

Compounding frequency affects how often interest is calculated and added to the principal, with more frequent compounding leading to a higher effective interest rate over time.

How did Maria's investment grow over 10 years with a principal of $6,154 at an 8% interest rate?

Maria's investment grew to approximately $13,695.00 after 10 years, using the formula for continuous compounding.

What steps are involved in calculating the time it takes for an investment to reach a certain value?

To calculate the time, rearrange the formula to t = (log(F/P) / (log(e)/r)) and substitute the future value, principal, and interest rate.

What was the initial investment required for John to reach a future value of $1,912.41 after 15 years at 0.63% interest?

John's initial investment needed to be approximately $1,289.00 to reach a future value of $1,912.41 after 15 years.