SUMMARY
The compound interest formula for continuously compounded interest is defined as A = P0ert, where A is the amount, P0 is the principal, r is the interest rate, and t is time in years. A participant in the discussion incorrectly proposed A(t) = 500 × 6.5t as the formula, leading to confusion regarding the base of the exponent. The correct understanding is that the base e is used for continuous compounding, as established in financial mathematics. Resources such as Khan Academy provide further clarification on this topic.
PREREQUISITES
- Understanding of the compound interest formula
- Familiarity with the mathematical constant e
- Basic knowledge of exponential functions
- Concept of continuous compounding in finance
NEXT STEPS
- Study the derivation of the formula A = P0ert for continuous compounding
- Explore Khan Academy's resources on continuously compounding interest
- Learn about the differences between discrete and continuous compounding
- Investigate real-world applications of continuous compounding in finance
USEFUL FOR
Students studying finance, educators teaching compound interest, and anyone interested in understanding the mathematics of continuous compounding.
