Final answer:
The question is about calculating the future value of an investment based on compound interest. Using the compound interest formula, where the interest rate is 9% and the time is 25 years, you can find the amount available for early retirement. The future value is calculated as A = q(1 + 0.09)^25.
Step-by-step explanation:
The student is asking about how to calculate the future value of a lottery winning invested at an interest rate of 9% over 25 years. This problem can be solved using the compound interest formula, which is:
A = P(1 + r/n)nt
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Assuming the interest is compounded annually (n=1), the formula simplifies to:
A = P(1 + r)t
If q represents the lottery winnings, then after 25 years, the amount available would be:
A = q(1 + 0.09)25
You would replace q with the actual amount of the lottery winnings to calculate the future value of the investment.