Question

A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously. Using the formula V=Pe⁽ʳᵗ⁾ , 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 7 years.

Answer 1

To calculate the future value of an investment compounded continuously, the formula V = Pe^(rt) is used. By substituting the given principal amount, annual rate, and time period into the formula, the future value is found to be approximately $784.73 after 7 years.

Step-by-step explanation:

The subject of this question is Mathematics, specifically in the area of compound interest with continuous compounding. To determine the amount of money in the investment account after 7 years, we will use the formula V = Pert, commonly used for continuous compounding interest problems.

The principal (P) in this scenario is $398, the rate (r) is 9.7% expressed as a decimal 0.097, and the time (t) is 7 years. Plugging these values into the formula gives us:

V = 398e(0.097 × 7)

Calculating the exponent part using a calculator equipped to handle the natural exponent (e), we get:

V ≈ 398e0.679

Continuing with the calculation:

V ≈ 398 × 1.972

V ≈ $784.73 when rounded to the nearest cent.

Thus, after 7 years, the amount of money in the account, compounded continuously at an annual rate of 9.7%, is approximately $784.73.