The value of Tessa's investment after 7 years, rounded to the nearest cent, is approximately $7320.95.
The formula for compound interest compounded continuously is given by the formula:
A=P⋅e^{rt}
where:
A is the future value of the investment/loan, including interest.
P is the principal amount (the initial amount of money).
e is the mathematical constant approximately equal to 2.71828.
r is the annual interest rate (as a decimal).
t is the time the money is invested or borrowed for, in years.
In this case:
P = $5500,
r=0.041 (4.1% expressed as a decimal),
t=7 years.
Now, let's plug in these values into the formula:
A=5500⋅e^{0.041⋅7}
Using a calculator, we can find the value of this expression:
A≈5500⋅e^{0.287}
A≈5500⋅1.3329.
A≈7320.95.
Therefore, the value of Tessa's investment after 7 years, rounded to the nearest cent, is approximately $7320.95.