Chapter 6.6, Problem 3GP

To determine

To Find:

How much would the price increase in 9 months.

Answer to Problem 3GP

  $\text{\$ 0}\text{.12}$

Explanation of Solution

Given:

Suppose a gallon of milk costs $2.99 now.

Inflation rate = 5.3%

Time = 9 months

Concept Used :

The formula $C=c{\left(1+r\right)}^n$ can be used to estimate the future cost of an item due to inflation.

C = the future cost

c = current cost

r = rate of inflation

n = number of years for the projection

Calculation:

• $\begin{array}{l}Given:\\ C=c{\left(1+r\right)}^n\\ C=\text{future cost}\\ \text{c = current cost = \$2}\text{.99}\\ \text{r = rate of inflation = 5}\text{.3\% = 0}\text{.053}\\ \text{n = number of years for the projection = }\frac{9}{12}=\frac{3}{4}\mathrm{......}[1year=12months]\\ \text{Substitute all the values in the equation and find the future cost:}\\ C=c{\left(1+r\right)}^n\\ =2.99{\left(1+0.053\right)}^{\frac{3}{4}}\\ \approx 3.11\\ \text{Price of a gallon of milk after 9 months is about \$3}\text{.11}\text{.}\\ \text{So, in 9 months , the price of a gallon of milk will increase by}\\ \text{\$3}\text{.11- \$2}\text{.99 = \$ 0}\text{.12 or 12 cents more than the current price}\text{.}\end{array}$