To solve this problem, let's use the compound interest formula. The compound interest formula is used to find the amount of money that will grow after a certain period of time with a certain interest rate. The formula is:
[tex]\[ A = P(1 + r)^t \][/tex]
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form).
- [tex]\( t \)[/tex] is the time the money is invested or borrowed for, in years.
Given in the question:
- [tex]\( P = 250 \)[/tex] dollars (the initial investment)
- [tex]\( r = 0.09 \)[/tex] (9% annual interest rate)
- [tex]\( t = 15 \)[/tex] years
Let's plug these values into the formula:
[tex]\[ A = 250 \times (1 + 0.09)^{15} \][/tex]
[tex]\[ A = 250 \times (1.09)^{15} \][/tex]
After calculating the above expression, the investment amount ([tex]\( A \)[/tex]) rounds to approximately [tex]$910.62.
Therefore, the closest answer to this value is:
A. $[/tex]911
