The price of milk is currently $3.89 per gallon and has been increasing by 5% per year. We need to calculate the price of milk in 10 years (part a) and the price of milk 5 years ago (part b).

1. Problem Description

The price of milk is currently $3.89 per gallon and has been increasing by 5% per year. We need to calculate the price of milk in 10 years (part a) and the price of milk 5 years ago (part b).

2. Solution Steps

a. Price in 10 years:

We can use the formula for compound interest to calculate the price in 10 years:

$FutureValue = PresentValue * (1 + rate)^{years}$

Here, $PresentValue = 3.89$, $rate = 0.05$, and $years = 10$.

$FutureValue = 3.89 * (1 + 0.05)^{10}$

$FutureValue = 3.89 * (1.05)^{10}$

$FutureValue = 3.89 * 1.62889462678$

$FutureValue = 6.33659011411$

Rounding to two decimal places, the price in 10 years will be approximately $6.

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b. Price 5 years ago:

We can use a similar formula, but this time we are solving for the PresentValue, given the FutureValue.

$FutureValue = PresentValue * (1 + rate)^{years}$

Rearranging the formula to solve for the PresentValue:

$PresentValue = \frac{FutureValue}{(1 + rate)^{years}}$

Here, $FutureValue = 3.89$, $rate = 0.05$, and $years = 5$.

$PresentValue = \frac{3.89}{(1 + 0.05)^{5}}$

$PresentValue = \frac{3.89}{(1.05)^{5}}$

$PresentValue = \frac{3.89}{1.2762815625}$

$PresentValue = 3.04795738463$

Rounding to two decimal places, the price 5 years ago was approximately $3.

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3. Final Answer

a. The price of milk in 10 years will be approximately $6.

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4. b. The price of milk 5 years ago was approximately $3.

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