Chapter 5.7, Problem 57AYU

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 inflation rate averages $3\%$, how much will $\$1000$ purchase in 2 years?

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 Inflation rate averages $3\%$, how much will $\$1000$ purchase in 3 years?

Answer to Problem 57AYU

Solution:

The purchasing power of $\$1000$ in 2 years is $\$940.9$.

Explanation of Solution

Given:

$P=1000, r=3\%$ and $n=2$

Calculation:

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

$A=1000{\left(1-0.03\right)}^2$

$=940.9$

Therefore, the purchasing power of $\$1000$ in 2 years is $\$940.9$.