Question

$920 is invested in an account earning 7.3% 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 attempt 1 out of 2 function: f(t) = ( )

Explanation:

Step1: Recall continuous compound formula

The formula for continuous compounding is $A(t) = Pe^{rt}$, where $P$ is principal, $r$ is APR, $t$ is time.

Step2: Substitute given values

$P = 920$, $r = 0.073$. So $f(t) = 920e^{0.073t}$. Round $e^{0.073}$ to 4 decimals: $e^{0.073} \approx 1.0757$. Rewrite as $f(t) = 920(1.0757)^t$.

Step3: Calculate APY

APY for continuous compounding is $APY = e^r - 1$. Substitute $r=0.073$: $APY = e^{0.073} - 1$.
<Expression>
$APY \approx 1.0757 - 1 = 0.0757$
</Expression>
Convert to percentage and round to hundredth of a percent: $0.0757 \times 100 = 7.57\%$.

Answer:

Function: $f(t) = 920(1.0757)^t$
Annual percentage yield (APY): $7.57\%$