Question

Jill opens a savings account that

compounds interest yearly. The value of
Jill's account is given by the equation,
A(y) = 175(1.0211)'.
What is the growth rate of the value of her
account?

Answer 1

The growth rate of Jill's account is approximately 2.09%.

Step-by-step explanation:

The growth rate of Jill's savings account can be calculated using the compound interest formula:

A = P(1 + r/n)^(nt)

• A represents the final amount
• P is the initial principal (175)
• r is the interest rate (0.0211)
• n is the number of compounding periods per year (1)
• t is the number of years (y).

To find the growth rate, we need to differentiate the equation with respect to time (y) and evaluate it when y = 0.

This will give us the rate of change of the account value with respect to time, which represents the growth rate.

Differentiating the equation gives us dA/dy = 175 * (1 + 0.0211)^y * ln(1.0211).

Evaluating this expression at y = 0 gives us the growth rate as ln(1.0211).

Therefore, the growth rate of Jill's account is approximately 0.0209, which is equivalent to 2.09%.