Question

Suppose that $500 is invested at an annual interest rate of 5.6% find the final amount of the investment after 10 years for interest compounded continuuously

Answer 1

To find the final amount of the investment after 10 years with continuous compounding, use the formula: A = P₀e^(rt). Substituting the given values, the final amount is approximately $847.46.

Step-by-step explanation:

To find the final amount of the investment after 10 years with continuous compounding, we can use the formula:

A = P₀e^(rt)

Where:

• A is the final amount
• P₀ is the principal amount ($500)
• e is the base of the natural logarithm (approximately 2.71828)
• r is the annual interest rate (5.6% or 0.056)
• t is the number of years (10)

Substituting these values into the formula, we get:

A = 500 * e^(0.056 * 10)

Calculating this expression, the final amount of the investment after 10 years with continuous compounding is approximately $847.46.