Question

average health premiums have been increasing at a rate of 5% per year. if an average familys premiums are $11,430 this year, what will they be in 2 years? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify compound growth formula

We use the compound amount formula: $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the annual growth rate, and $t$ is time in years.

Step2: Plug in given values

$P = 11430$, $r = 0.05$, $t = 2$
$A = 11430(1 + 0.05)^2$

Step3: Calculate the growth factor

First compute $(1.05)^2 = 1.1025$

Step4: Compute final premium

$A = 11430 \times 1.1025$
$A = 12591.575$

Step5: Round to nearest cent

Round $12591.575$ to two decimal places: $12591.58$

Answer:

$12591.58$