Question

The average American spent $8,508 on health care in 2011. The cost of health care is projected to rise about 5.8% per year for the years 2012-2022. Calculate the projected amount the average American spent on health care in 2014

Answer 1

The projected amount the average American spent on health care in 2014  is $ 10075.91

Solution:

Given that,

The average American spent $8,508 on health care in 2011

The cost of health care is projected to rise about 5.8% per year for the years 2012-2022

The increasing function is given as:

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate in decimal

t is number of years

From given,

a = 8508

$r = 5.8 \% = \frac{5.8}{100} = 0.058$

t = 2011 to 2014 = 3 years

Substituting the values, we get,

$y = 8508(1 + 0.058)^3\\\\y = 8508(1.058)^3\\\\y = 8508 \times 1.1842\\\\y = 10075.914 \approx 10075.91$

Thus the projected amount the average American spent on health care in 2014  is $ 10075.91