To calculate the future value of an investment with continuous compounding, you can use the formula:
\[ A = P \times e^{rt} \]
Where:
- \( A \) is the future value of the investment
- \( P \) is the initial investment amount (principal), which is $1,500 in this case
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828
- \( r \) is the annual interest rate in decimal form, which is 2.6% or 0.026
- \( t \) is the time the money is invested for, which is 6 years in this scenario
Substitute the given values into the formula:
\[ A = 1500 \times e^{0.026 \times 6} \]
Calculate the exponent part first:
\[ 0.026 \times 6 = 0.156 \]
\[ e^{0.156} \approx 1.169072 \]
Now, multiply the initial investment by the calculated exponential value:
\[ 1500 \times 1.169072 \approx 1753.608 \]
Rounded to the nearest cent, you would have approximately $1753.61 in your account after 6 years with continuous compounding.
