Final answer:
Using the continuous compounding formula A = Pe^(rt), where P is the principal amount of $1,854, r is 3% per year (as a decimal 0.03), e is the mathematical constant, and t is 5 years, the balance after 5 years would be approximately $2,152.67.
Step-by-step explanation:
The calculation of compound interest that is compounded continuously uses the formula A = Pert, where:
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (as a decimal)
- t is the time in years
- e is the constant approximately equal to 2.71828
In this problem, the principal P is $1,854.00, the annual interest rate r is 3% or 0.03, and the time t is 5 years. Plugging the values into the formula, we get:
A = 1854 * e(0.03*5)
To find the account balance after 5 years, you would calculate:
A ≈ $1,854 * e(0.15)
Using a calculator with an exponent function for the constant e, you find:
A ≈ $1,854 * 1.1618342 = $2,152.67
Therefore, the balance after 5 years will be approximately $2,152.67 assuming a continuous compound interest.