To determine how much the investment will be worth in 10 years if \[tex]$535 is invested at an interest rate of 6% per year, and is compounded continuously, we will use the continuous compound interest formula:
\[ A = Pe^{rt} \]
where:
- \( P \) is the principal amount (initial investment)
- \( r \) is the annual interest rate (as a decimal)
- \( t \) is the time the money is invested for, in years
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828
Given:
- \( P = 535 \)
- \( r = 0.06 \) (6% as a decimal)
- \( t = 10 \) years
We can now substitute these values into the formula:
\[ A = 535 \times e^{0.06 \times 10} \]
\[ A = 535 \times e^{0.6} \]
When we calculate \( e^{0.6} \), we find that it is approximately equal to 1.82212.
\[ A = 535 \times 1.82212 \]
Multiplying these values:
\[ A \approx 535 \times 1.82212 = 974.83 \]
Therefore, the investment will be worth approximately \(\$[/tex] 974.83\) after 10 years.
Thus, the correct answer is:
[tex]\(\boxed{\$ 974.83}\)[/tex]
