Question

A person places $133 in an investment account earning an annual rate of 5.8%, compounded continuously. Using the formula V, equals, P, e, start superscript, r, t, end superscriptV=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 9 years.

Answer 1

Using the formula for continuously compounded interest, the investment of $133 at an annual rate of 5.8% will grow to approximately $224.42 after 9 years.

Step-by-step explanation:

To calculate the amount of money in an investment account after 9 years with an annual interest rate of 5.8%, compounded continuously, we use the formula V = Pert. In this formula, V is the future value of the investment, P is the principal amount ($133), e is the base of the natural logarithm (approximately 2.7183), r is the annual interest rate (5.8% or 0.058 as a decimal), and t is the time in years (9).

The calculation for the future value of the investment would therefore be:

V = 133e(0.058 × 9)

Using a calculator, we can find the value of e to the power of (0.058 × 9):

e(0.058 × 9) ≈ e0.522 ≈ 1.6856

So the future value V is:

V ≈ 133 × 1.6856 ≈ $224.42

Thus, the amount of money in the investment account after 9 years, to the nearest cent, is $224.42.