Question

$540 is invested in an account earning 9.1% interest (APR), compounded

continuously. 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: The formula for continuously compounded interest is given by:

A = P * e^(rt)

Where:

A = the final account balance

P = the initial investment (principal)

r = the annual growth rate as a decimal

t = the number of years the investment is held

In this case, P = 540, r = 0.091 and t = t years.

So, the function showing the value of the account after t years is:

A = 540 * e^(0.091t)

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

APY = (e^r - 1) * 100

Substituting r = 0.091, we find:

APY = (e^0.091 - 1) * 100 = 9.56%

So, the APY is approximately 9.56%, to the nearest hundredth of a percent.

Explanation: