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

average health premiums have been increasing at a rate of 9% per year. if an average familys 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 familys 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 (in decimal), and $t$ is the number of years. Here, $P = 10630$, $r = 0.09$ (since 9% = 0.09), and $t = 6$.

Step2: Substitute the values into the formula

Substitute $P = 10630$, $r = 0.09$, and $t = 6$ into the formula: $A = 10630(1 + 0.09)^6$

Step3: Calculate $(1 + 0.09)^6$

First, calculate $1 + 0.09 = 1.09$. Then, $1.09^6 \approx 1.67710011$ (using a calculator).

Step4: Multiply by the principal amount

Multiply $10630$ by $1.67710011$: $A = 10630 \times 1.67710011 \approx 10630 \times 1.6771 \approx 17827.573$

Step5: Round to the nearest cent

Rounding $17827.573$ to the nearest cent gives $17827.57$.

Answer:

$17827.57$