Final answer:
To calculate the amount of money that can be withdrawn at the end of the investment period, we need to use compound interest calculations. First, we calculate the future value of the $4,000 annual investment at 5% interest for 3 years. Then, we take this future value and compound it for an additional 5 years at 8% interest. The final amount that can be withdrawn is $17,639.74.
Step-by-step explanation:
To calculate the amount that can be withdrawn at the end of the investment period, we will use the concept of compound interest. Here's how we can calculate it:
For the first 3 years, we need to compound the annual investment of $4,000 at 5% per year. Using the formula for the future value of an ordinary annuity, we get:
FV = P * [(1 + r)^n - 1] / r
Where FV is the future value, P is the investment amount, r is the interest rate, and n is the number of years. Plugging in the values, we have:
FV = $4,000 * [(1 + 0.05)^3 - 1] / 0.05
Simplifying, we find that the future value after 3 years is $12,613.47.
Next, we take this future value and shift it into an investment paying 8% per year for 5 additional years. Using the compound interest formula, we can calculate the value at the end of the 5 years:
FV = P * (1 + r)^n
Plugging in the values, we have:
FV = $12,613.47 * (1 + 0.08)^5
Simplifying, we find that the future value after 5 years is $17,639.74.
Therefore, the amount of money that can be withdrawn at the end of the investment period is $17,639.74.