Question

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 5% each year. In other words, if you have $1 this year, next year it will only buy you $0.95 worth of stuff. How much will $100 buy you in 15 years?

Answer 1

$46.33

Explanation :

Let the value of $100 after 15 years be x .

It says that inflation rate per year is 5% thus inflation rate after 15 years would be the product of present value and rate of inflation deduct from 1 raised to the power of number of years thus,

• x = $100*(1-0.05)^15
• x = $100*(0.95)^15
• x = $100*0.46329
• x ≈ $46.329

thus, after 15 years $100 would get us stuff worth of $46.33 (2 d.p.)

Answer 2

$46.33

Explanation:

To calculate the future value of money considering inflation, we can use the formula for compound interest in reverse. In this case, it's a decrease due to inflation, so we use the formula:

`\sf FV = PV * (1 - r)^t`

Where:

• 
  `\sf FV` is the future value (what $100 will buy we in the future),
• 
  `\sf PV` is the present value (initial amount of money, $100 in this case),
• 
  `\sf r` is the rate of decrease due to inflation per year (5%, or 0.05 in decimal form), and
• 
  `\sf t` is the number of years (15 years in this case).

Now, substitute the values:

`\sf FV = 100 * (1 - 0.05)^(15)`

Calculate this expression to find the future value:

`\sf FV = 100 * (0.95)^(15)`

`\sf FV \approx 100 * 0.4632912302`

`\sf FV \approx 46.32912302`

`\sf FV \approx 46.33 \textsf{( in 2 d.p.)}`

Therefore, 100 will buy approximately $46.33 worth of goods in 15 years, considering a 5% annual decrease in the value of money due to inflation.