Final answer:
To determine the future value of an annual $2,000 investment made between the ages of 22 and 49 at an 8% annual interest rate, the formula for the future value of an ordinary annuity is applied. After plugging in the annual investment amount, interest rate, and number of years, the future value on the 50th birthday is approximately $205,931.87. Hence, the correct option is $205,931.87.
Step-by-step explanation:
When planning for the future, understanding the concept of compound interest is vital, as it significantly amplifies the growth of savings over time. In this case, you aim to invest $2,000 annually from your 22nd birthday until your 49th birthday and want to determine the value of this investment on your 50th birthday, assuming an 8% annual return. The investment scenario can be solved using the formula for the future value of an annuity, where payments are made at the end of each period.
First, we'll calculate the number of payments you'll be making. From age 22 to 49, inclusive, you'll be investing for 28 years. The future value of an ordinary annuity can be found using the formula:
FV = P * [(1 + r)^n - 1] / r
where FV is the future value of the annuity, P is each annual payment, r is the annual interest rate, and n is the number of payments.
Applying these values:
- P = $2,000
- r = 0.08 (or 8%)
- n = 28
So the formula becomes:
FV = 2000 * [(1 + 0.08)^28 - 1] / 0.08
After calculating, the future value comes out to be approximately $205,931.87. Therefore, the correct answer from the provided options is $205,931.87.