Chapter 5.7, Problem 59AYU

Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is $3\%$, then $\$1000$ worth of purchasing power now will have only $\$970$ worth of purchasing power in 1 year because $3\%$ of the original $\$1000\left(0.03\times 1000=30\right)$ has been eroded due to inflation. In general, if the rate of inflation averages $r$ per annum over $n$ years, the amount $A$ that $\$P$ will purchase after $n$ years is $A=P·{(1-r)}^n$ where $r$ is expressed as a decimal.

Inflation If the amount that $\$1000$ will purchase is only $\$950$ after 2 years, what was the average inflation rate?

To determine

To find: Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is $3\%$, then $\$1000$ worth of purchasing power now will have only $\$970$ worth of purchasing power in 1 year because $3\%$ of the original $\$1000$ $\left(0.03\times 1000=30\right)$ has been eroded due to inflation. In general, if the rate of inflation averages $r$ per annum over $n$ years, the amount $A$ that $\$P$ will purchase after $n$ years is $A=P\cdot {(1-r)}^n$ where $r$ is expressed as a decimal. Inflation If the amount that $\$1000$ will purchase is only $\$950$ after 2 years, what was the average inflation rate?

Answer to Problem 59AYU

Solution:

The average inflation rate is $2.53\%$.

Explanation of Solution

Given:

$P=1000, A=950$ and $n=2$

Calculation:

$A=P{\left(1-r\right)}^n$

$950=1000{\left(1-r\right)}^2$

${\left(1-r\right)}^2=\frac{950}{1000}$

$1-r=0.9747$

$r=0.0253$

$r=2.53\%$

Therefore, the average inflation rate is $2.53\%$.