Final answer:
Using the compound interest formula with a principal amount of $2000, an annual interest rate of 9%, and a time period of 21 years, the future value is calculated to be approximately $11,969.44. However, this does not match any of the provided options, suggesting there might be a miscalculation or a typo in the options given.
Step-by-step explanation:
To calculate the value in 21 years of a $2000 deposit earning nine percent per year, we use the formula for compound interest.
The formula for the future value of an investment earning compound interest is:
FV = P × (1 + r)^n
Where:
- FV is the future value of the investment
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (decimal)
- n is the number of years the money is invested
For this question:
- P = $2000
- r = 9% or 0.09
- n = 21 years
Thus, the calculation is:
FV = $2000 × (1 + 0.09)^{21}
FV = $2000 × (1.09)^{21}
Now, using a calculator, we can find the future value:
$2000 × (1.09)^{21} ≈ $2000 × 5.984719 = $11,969.44
However, this value does not match any of the provided options (A) $12,217.62 (B) $11,784.14 (C) $19,759.04 (D) $29,363.62. It appears that there might be a miscalculation or a typo. Therefore, it is important to double-check the calculation or to clarify the options provided.