The future value of an investment after 4 years with continuous compound interest at an 8% annual rate and an initial principal of $748 is approximately $1,030.64.
The question involves calculating the future value of an investment with continuous compound interest. We can find the amount of money in the account after 4 years by using the given formula V = Pert, where V is the future value of the investment, P is the principal amount ($748), e is the base of the natural logarithm, r is the annual interest rate (0.08), and t is the time in years (4).
The calculation is as follows:
V = 748 * e^(0.08 * 4)
To solve this, we use a calculator with a function for e to the power of a number (exponentiation). After performing the calculation:
V ≈ 748 * e^(0.32)
V ≈ 748 * 1.37712776
V ≈ $1,030.64
Therefore, the amount of money in the account after 4 years, to the nearest cent, is approximately $1,030.64.