Final answer:
The total account balance after 23 years with a principal of $830 and an annual interest rate of 3.72%, compounded continuously, is approximately $1,952.49. The closest answer provided is $1,952.81.
Step-by-step explanation:
To calculate the future value of an investment with continuous compound interest, we use the formula A = Pert, where:
- P is the principal amount ($830 in this case)
- r is the annual interest rate (expressed as a decimal, so 3.72% becomes 0.0372)
- t is the time in years (23 years in this case)
- e is the base of the natural logarithm, approximately equal to 2.71828
Applying these values to the formula gives us the total account balance after 23 years:
A = 830e(0.0372)(23)
Calculating the exponent:
0.0372 * 23 = 0.8556
Now calculating the entire expression:
A = 830 * e0.8556
Using a calculator, e0.8556 is approximately equal to 2.3512. Therefore:
A = 830 * 2.3512
A ≈ 1952.49
The total balance in the account after 23 years is approximately $1,952.49, making the closest answer $1,952.81.