Suppose 10,000 is invested at an annual rate of 5% for 10...

Suppose $\$ 10,000$ is invested at an annual rate of 5$\%$ for 10 years. Find the future value if interest is compounded as follows.
a. Annually
b. Quarterly
c. Monthly
d. Daily (365 days)
e. Continuously

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Key Concepts

Discrete Compounding

Discrete compounding involves adding interest to the principal at specific intervals such as annually, quarterly, monthly, or daily. The future value is calculated using the formula A = P(1 + r/n)^(n*t), where r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. This method shows how different compounding frequencies affect the accumulation of interest over time.

Continuous Compounding

Continuous compounding extends the concept of compounding by assuming that interest is added an infinite number of times per year, leading to the formula A = P*e^(r*t). Here, e is the base of natural logarithms, and this approach represents the theoretical limit of compounding frequency, resulting in the maximum possible accumulation of interest over a given period.

Compound Interest

Compound interest is the process where interest earned on an investment is reinvested so that, in future periods, interest is earned on the original principal as well as on the accumulated interest. This results in exponential growth over time, making compound interest a fundamental concept in financial mathematics and investment planning.

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