Question

7. The future value that accrues when $500 is invested at 9%, compounded continuously, is S(t)=500e 0.09t

where t
​
is the number of years. At what rate is the money in this account growing when t=4 ? (Round your answers to the nearest cent.)

Answer 1

The rate at which the money in the account is growing when t=4 is approximately $398.86.

Step-by-step explanation:

The formula for continuous compound interest is given by the function S(t) = P * er * t, where P is the principal amount, r is the interest rate, and t is the number of years.

In this case, the principal amount is $500 and the interest rate is 9% (or 0.09). Plugging these values into the formula, we get S(t) = 500 * e0.09t.

To find the rate at which the money is growing when t = 4, we need to find the derivative of the function S(t) with respect to t. Differentiating S(t) = 500 * e0.09t gives us the rate of growth, which is 500 * 0.09 * e0.09t.

Substituting t = 4 into the formula, we get the rate of growth at t = 4 to be 500 * 0.09 * e0.09 * 4.

Calculating this value gives us the rate of growth to be approximately $398.86.