Questions: The future value of 0.25 growing at 10.75 percent per year for 15 years is formula: FV = PV x (1+r)^n.

Solution Steps

To find the future value of a lump sum, we can use the formula \( FV = PV \times (1 + r)^n \), where:

• \( PV \) is the present value (initial amount),
• \( r \) is the annual growth rate,
• \( n \) is the number of years.

Given:

• \( PV = 0.25 \) dollars,
• \( r = 10.75\% = 0.1075 \),
• \( n = 15 \) years.

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

We are given the following values:

• Present Value (\( PV \)) = \$0.25
• Annual Growth Rate (\( r \)) = 10.75% = 0.1075
• Number of Years (\( n \)) = 15

The future value (\( FV \)) is calculated using the formula: \[ FV = PV \times (1 + r)^n \]

Substituting the given values into the formula, we get: \[ FV = 0.25 \times (1 + 0.1075)^{15} \]

Performing the calculation: \[ FV = 0.25 \times (1.1075)^{15} \] \[ FV \approx 0.25 \times 4.6255 \] \[ FV \approx 1.1564 \]

Final Answer