Question

A person places $6520 in an investment account earning an annual rate of 2.5%, compounded continuously. Using the formula V = Pe^{rt}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 3 years

Answer 1

To determine the value of an investment account after 3 years with an annual interest rate of 2.5% compounded continuously, you use the formula V = Pert. The future value of the investment will be approximately 7029.96.

Step-by-step explanation:

The question deals with compound interest compounded continuously. To find the value of the investment after 3 years, we use the formula V = Pert.

Using the given values:

P (Principal) = 6520

r (Annual interest rate) = 2.5% or 0.025

t (Time in years) = 3

e (Base of natural logarithms) ≈ 2.71828

Now, we calculate the future value of the investment:

V = 6520 * e(0.025*3)

To get the value to the nearest cent, calculate the exponential term using a calculator with capabilities for continuous compounding. Plugging in the values, we get:

V ≈ 6520 * e(0.075)

V ≈ 6520 * 1.078

V ≈ $7029.96

The account will have approximately 7029.96 after 3 years, to the nearest cent, earning an annual rate of 2.5% compounded continuously.

Answer 2

The amount of money, to the nearest cent, in the account after 3 years will be $ 7028.56

Step-by-step explanation:

The amount is given by

Given P = $6520

r = 2.5%

t = 3 years

Substituting the given values, we get -

The amount of money, to the nearest cent, in the account after 3 years will be $ 7028.56