Lost at derivatives

Question

Suppose you deposit 300 dollars into a bank with 6% simple interest. The amount in the account after years is given by A(t)=300(1.06)^t . (in dollars)

a. What is the average rate of change for the first year?

Rate (in dollars per year): ______

b. What is the average rate of change for the first five years?

Rate (in dollars per year): ______

c. . What is the average rate of change for the first ten years?

Rate (in dollars per year): ______

Answer 1

A(t) = 300(1.06)^t

Average rate of change for the first year = [A(1) - A(0)] / (1-0) = (318 - 300) / 1 = $18 per year

Average rate of change for the first 5 years = [A(5) - A(0)] / (5 - 0) = {401.47 - 300] / 5 = $20.29 per year

Average rate of change for the first 10 years = [A(10) - A(0)] / (10 0) = [537.25 - 300] / 10 = $23.73 per year

Answer 2

The formula I use is fv=p(1+int/c)^(nt).

fv future value

p principal 300

int .06

c compound 1

n years 1, 5, 10

times/yr 1

1yr=$318

5 =401.47

10 =537.25

Your formula=318, 401.47, 537.25