Question

A person places $748 in an investment account earning an annual rate of 8%,

compounded continuously. Using the formula V = Pert, where V is the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 4 years.

Answer 1

239.36

Explanation:

you do the 8 precent times 4 years =32 precent

then you calculate 32 % out of the 748 $ and the answer is 239.36 dollar

Answer 2

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.