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?
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Answers
GPT-4o mini
To calculate the health premiums in 6 years given an annual increase of 9%, you can use the formula for compound interest:
\[
P = P_0 (1 + r)^t
\]
where:
- \(P_0\) is the current premium amount,
- \(r\) is the annual increase rate (as a decimal),
- \(t\) is the number of years into the future,
- \(P\) is the future premium amount.
In your case:
- \(P_0 = 10,630\)
- \(r = 0.09\)
- \(t = 6\)
Now, plug in the values:
\[
P = 10,630 \times (1 + 0.09)^6
\]
Calculating \(1 + 0.09\):
\[
1 + 0.09 = 1.09
\]
Now, calculate \(1.09^6\):
\[
1.09^6 \approx 1.6771
\]
Now, multiply by the current average premiums:
\[
P \approx 10,630 \times 1.6771 \approx 17,762.66
\]
Therefore, after rounding, the average health premiums for the family in 6 years will be approximately **$17,763**.
\[
P = P_0 (1 + r)^t
\]
where:
- \(P_0\) is the current premium amount,
- \(r\) is the annual increase rate (as a decimal),
- \(t\) is the number of years into the future,
- \(P\) is the future premium amount.
In your case:
- \(P_0 = 10,630\)
- \(r = 0.09\)
- \(t = 6\)
Now, plug in the values:
\[
P = 10,630 \times (1 + 0.09)^6
\]
Calculating \(1 + 0.09\):
\[
1 + 0.09 = 1.09
\]
Now, calculate \(1.09^6\):
\[
1.09^6 \approx 1.6771
\]
Now, multiply by the current average premiums:
\[
P \approx 10,630 \times 1.6771 \approx 17,762.66
\]
Therefore, after rounding, the average health premiums for the family in 6 years will be approximately **$17,763**.