Question

If $1,000 is invested in an account that pays 5% interest compounded annually, an expression that represents the amount in the account at the end of five years can be given by which of the following equations?

A. 1000(0.5)
B. 1000 + (0.3)
C. 1000(1 + 0.05)^5

Answer 1

The correct expression for the amount in an account after five years with a 5% annual interest rate compounded annually is 1000(1 + 0.05)^5.

Step-by-step explanation:

If $1,000 is invested in an account that pays 5% interest compounded annually, the expression that represents the amount in the account at the end of five years is C. 1000(1 + 0.05)^5. This is because with compound interest, the interest is calculated not just on the initial principal but also on the accumulated interest from previous periods.

To calculate the future value of this investment, we use the compound interest formula, which is Principal * (1 + Interest Rate)^Number of Periods. Given a principal of $1,000, an annual interest rate of 5% (or 0.05 in decimal form), and a period of 5 years, the calculation would be $1,000 * (1 + 0.05)^5.