QuestionBetween 2005 and 2010, the average rate of inflation was about $3.2 \%$ per year (as measured by the Consumer Price Index). If a cart of groceries cost $\$ 150$ in 2005 , what did it cost in $2010 ?$

Studdy Solution
Apply the formula to find the cost in 2010.
Given: - $PV = 150$ - $r = 0.032$ (since $3.2\%$ is equivalent to $0.032$) - $n = 5$ (from 2005 to 2010)
Substitute these values into the formula:
$$FV = 150 \times (1 + 0.032)^5$$
Calculate $FV$:
$$FV = 150 \times (1.032)^5$$
$$FV \approx 150 \times 1.1705$$
$$FV \approx 175.575$$
The cost of the groceries in 2010 is approximately:
$\boxed{\$175.58}$