Question

The future value that accrues when $700 is invested at 5%, compounded continuously, is S(t)=700e⁰.⁰⁵ᵗ

where t is the number of years. (Round your answers to the nearest cent.)
(a) At what rate is the money in this account growing when t=6 ?

Answer 1

To find the rate at which the money is growing when t = 6, we need to take the derivative of the continuous compound interest formula and solve for the rate.

Step-by-step explanation:

The formula for continuous compound interest is given as:

S(t) = P * e^(rt)

Where:

• S(t) is the future value
• P is the initial investment
• e is the mathematical constant approximately equal to 2.71828
• r is the interest rate
• t is the number of years

To find the rate at which the money is growing, we need to take the derivative of S(t) with respect to t:

S'(t) = P * r * e^(rt)

Substituting the given values P = 700 and t = 6, we have:

S'(6) = 700 * r * e^(6*r)

At t = 6, we can solve the equation to find the rate at which the money is growing.