Questions: Suppose you put 1000 in a savings account that offers a 2% annual interest rate. What will be the future value exactly 10 years later? (Round your answer to the nearest dollar)

Solution Steps

To find the future value of an investment with compound interest, we use the formula for compound interest: \( FV = P \times (1 + r)^n \), where \( FV \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate, and \( n \) is the number of years. In this case, \( P = 1000 \), \( r = 0.02 \), and \( n = 10 \).

We are given the principal amount \( P = 1000 \), the annual interest rate \( r = 0.02 \), and the number of years \( n = 10 \).

The future value \( FV \) of an investment with compound interest is calculated using the formula: \[ FV = P \times (1 + r)^n \] Substituting the given values: \[ FV = 1000 \times (1 + 0.02)^{10} \]

Calculate the expression: \[ FV = 1000 \times 1.02^{10} \approx 1218.9944 \]

Round the future value to the nearest dollar: \[ \text{Rounded } FV = 1219 \]

Final Answer