Question

average health premiums have been increasing at a rate of 9% per year. if an average family’s premiums are $10,630 this year, what will they be in 6 years? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual growth rate (in decimal), and $t$ is the number of years.

Step2: Convert the growth rate to decimal

The growth rate $r$ is 9%, which is $0.09$ in decimal.

Step3: Substitute the values into the formula

We have $P = 10630$, $r = 0.09$, and $t = 6$. So, $A = 10630(1 + 0.09)^6$.

Step4: Calculate $(1 + 0.09)^6$

First, $1 + 0.09 = 1.09$. Then, $1.09^6 \approx 1.67710011$.

Step5: Calculate the final amount

Multiply $10630$ by $1.67710011$: $10630\times1.67710011 \approx 17827.574173$.

Answer:

$\$17827.57$ (rounded to the nearest cent)