Question

$9, 100 is invested in an account earning

3% interest (APR), compounded quarterly.
Write a function showing the value of the
account after t years, where the annual
growth rate can be found from a constant
in the function. Round all coefficients in
the function to four decimal places. Also,
determine the percentage of growth per
year (APY), to the nearest hundredth of a
percent.

Answer 1

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

Where

A is the future value of the account

P is the initial principal amount, which is $9,100

r is the annual interest rate, which is 3%

n is the number of times the interest is compounded per year, which is 4 (quarters)

t is the number of years

So the function for the value of the account after t years is:

A = 9100(1 + 0.03/4)^(4t)

To determine the percentage of growth per year (APY), we can use the formula:

APY = ( (A/P)^(1/t) - 1) * n

In this case,

APY = ( (A/9100)^(1/t) - 1) * 4

APY represents the annual percentage yield, which is the interest rate taking compounding into account.

Please note that in the above expression the coefficient 0.03 is rounded to four decimal places as instructed.

Explanation: