Sebastian invested $32,000 in an account paying an interest rate of 2 5/8% compounded monthly. Avery invested $32,000 in an account paying an interest rate of 2 1/2% compounded continuously. After 18 years, how much more money would Sebastian have in his account than Avery, to the nearest dollar?

The amount that Sebastian has more than Avery is $1120

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

Considering Sebastian's investment,

P = 32000

r = 2.625% = 2.625/100 = 0.02625

n = 12 because it was compounded 12 times in a year.

t = 18 years

Therefore,.

A = 32000(1 + 0.02625/12)^12 × 18

A = 32000(1+0.0021875)^216

A = 32000(1.0021875)^216

A = 32000 × 1.603

A = 51296

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = 32000

r = 2.5% = 2.5/100 = 0.025

t = 18 years

Therefore,

A = 32000 x 2.7183^(0.025 x 18)

A = 32000 x 2.7183^(0.45)

A = 32000 × 1.568

A = 50176

The amount that Sebastian has more than Avery is

51296 - 50176 = $1120

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).