average health premiums have been increasing at a rate of 9% per year. if an average family’s premiums are…

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.

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.

Answer

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 interest rate (as a decimal), and $t$ is the number of years.

Step2: Convert the rate to a decimal

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

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

Step5: Multiply by the principal amount

$A = 10630 \times 1.67710011 \approx 17827.574163$.

Step6: Round to the nearest cent

Rounding $17827.574163$ to the nearest cent gives $17827.57$.

Answer:

$17827.57$