Questions: Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 2% each year. In other words, if you have 1 this year, next year it will only buy you 0.98 worth of stuff. How much will 100 buy you in 10 years?

Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 2% each year. In other words, if you have 1 this year, next year it will only buy you 0.98 worth of stuff. How much will 100 buy you in 10 years?
Transcript text: Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by $2 \%$ each year. In other words, if you have $\$ 1$ this year, next year it will only buy you $\$ 0.98$ worth of stuff. How much will $\$ 100$ buy you in 10 years?
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Solution

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Solution Steps

Step 1: Convert the annual inflation rate from a percentage to a decimal

The annual inflation rate as a decimal is 0.02.

Step 2: Subtract the decimal inflation rate from 1 to find the annual depreciation factor

The annual depreciation factor of the money's value is 0.98.

Step 3: Raise this depreciation factor to the power of n

After raising the depreciation factor to the power of 10, we get 0.817.

Step 4: Multiply the initial amount of money (P) by this factor

The future value of the money, before rounding, is 81.707.

Step 5: Round the result to the nearest specified decimal places

Final Answer: The future value of the money, in terms of its purchasing power, is 81.71.

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