Question

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.

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 time in years.

Step2: Convert the rate to decimal

The rate $r$ is 9%, so in decimal form, $r = \frac{9}{100} = 0.09$.

Step3: Identify the values of P, r, and t

Here, $P = 10630$, $r = 0.09$, and $t = 6$.

Step4: Substitute the values into the formula

$A = 10630(1 + 0.09)^6 = 10630(1.09)^6$.

Step5: Calculate $(1.09)^6$

First, calculate $1.09^6$. $1.09^2 = 1.1881$, $1.09^3 = 1.1881\times1.09 = 1.295029$, $1.09^4 = 1.295029\times1.09 = 1.41158161$, $1.09^5 = 1.41158161\times1.09 = 1.5386239549$, $1.09^6 = 1.5386239549\times1.09 = 1.677100110841$.

Step6: Calculate A

Now, multiply $10630$ by $1.677100110841$: $A = 10630\times1.677100110841 \approx 17827.573178$.

Step7: Round to the nearest cent

Rounding $17827.573178$ to the nearest cent gives $17827.57$.

Answer:

$\$17827.57$