To determine how much you will have after investing [tex]$\$[/tex]250[tex]$ at an annual interest rate of $[/tex]16\%[tex]$ for $[/tex]18[tex]$ years, you can use the compound interest formula. The compound interest formula is given by:
\[ A = P (1 + r)^t \]
where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in decimal form).
- \( t \) is the number of years the money is invested for.
Given:
- \( P = 250 \) dollars
- \( r = 0.16 \) (since $[/tex]16\%[tex]$ is equal to $[/tex]0.16[tex]$ in decimal form)
- \( t = 18 \) years
Plug these values into the compound interest formula:
\[ A = 250 (1 + 0.16)^{18} \]
First, simplify the term inside the parentheses:
\[ 1 + 0.16 = 1.16 \]
Now substitute back into the formula:
\[ A = 250 \times (1.16)^{18} \]
Next, calculate \( (1.16)^{18} \):
\[ (1.16)^{18} \approx 14.462514456854164 \]
Now multiply this result by the principal amount:
\[ A = 250 \times 14.462514456854164 \approx 3615.628614213541 \]
Therefore, the amount of money you will have after 18 years is approximately:
\[ \boxed{3615.63} \]
So, after investing $[/tex]\[tex]$250$[/tex] at a [tex]$16\%$[/tex] annual interest rate for [tex]$18$[/tex] years, you will have approximately [tex]$\$[/tex]3615.63$.
