Questions: Find the future value for a savings account with an initial deposit of 2500 at 4.5% interest for 10 years.

Solution Steps

To find the future value of a savings account with compound interest, we can use the formula: \[ FV = PV \times (1 + r)^n \] where:

• \( FV \) is the future value
• \( PV \) is the present value (initial deposit)
• \( r \) is the annual interest rate (as a decimal)
• \( n \) is the number of years

Given:

• \( PV = 2500 \)
• \( r = 4.5\% = 0.045 \)
• \( n = 10 \)

We will plug these values into the formula to calculate the future value.

We are given the following values:

• Initial deposit (\( PV \)) = \$2500
• Annual interest rate (\( r \)) = 4.5% = 0.045
• Number of years (\( n \)) = 10

To find the future value (\( FV \)) of the savings account, we use the formula: \[ FV = PV \times (1 + r)^n \]

Substitute the given values into the formula: \[ FV = 2500 \times (1 + 0.045)^{10} \]

Perform the calculation: \[ FV = 2500 \times (1.045)^{10} \] \[ FV \approx 2500 \times 1.552 \] \[ FV \approx 3882.42 \]

Final Answer