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.
To find the average health premiums in 6 years, we need to calculate the 6th iteration of increasing premiums at a rate of 9% per year.
Let's use the formula for calculating compound interest: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial premium amount)
r = the annual interest rate (9% or 0.09 in decimal form)
n = the number of times that interest is compounded per year (assuming once per year)
t = the number of years the money is invested or borrowed
Plugging in the given values, we have:
P = $10,630
r = 0.09
n = 1 (compounded once per year)
t = 6 (6 years)
A = 10,630(1 + 0.09/1)^(1*6)
A = 10,630(1.09)^6
A = 10,630(1.71817)
Calculating the result, we get:
A ≈ $18,275.75
Therefore, the average health premiums for an average family will be approximately $18,275.75 in 6 years.