Question

19. Inflation causes things to cost more, and for our money to buy less (hence yourgrandparents saying, "In my day, you could buy a cup of coffee for a nickel").Suppose inflation decreases the value of money by 5% each year. In other words, ifyou have $1 this year, next year it will only buy you $0.95 worth of stuff. How muchwill $100 buy you in 20 years?

Answer 1

Given the inflation rate of the value of item:

Let V = value of the money

after 20 yrs

In you have $1 this year, next it will only buy $0.95 item.

Using an exponential expression:

`1-0.05=0.95`
`\begin{gathered} V=100(0.95)^(20) \\ V=100(0.3585) \\ V=35.85 \end{gathered}`

Therefore

In 20 yrs $100 is worth $35.85