Question

If you invest $1,000 at an annual interest rate of 5% compounded continuously, calculate the final amount you have in the account after five years.

A) $3,162.28
B) $1,284.02
C) $1,122.01
D) $2,718.28

Answer 1

To calculate the final amount with continuous compounding, use the formula A = P*e^(rt), where A is the final amount, P is the principal, e is Euler's number, r is the interest rate, and t is the time period. Plugging in the values, the final amount is approximately $1,284.03.

Step-by-step explanation:

To calculate the final amount you have in the account after five years with continuous compounding, you can use the formula A = P*e^(rt), where A is the final amount, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate (expressed as a decimal), and t is the time period in years. In this case, P = $1,000, r = 0.05, and t = 5.

Plugging in the values, we get A = $1,000 * e^(0.05 * 5) = $1,000 * 2.71828^(0.25) = $1,000 * 1.2840254 = $1,284.03 (rounded to the nearest cent).

Therefore, the final amount you have in the account after five years is approximately $1,284.03. The correct answer is B) $1,284.02.