Chapter 5.7, Problem 62AE

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 average inflati on rate is $4\%$, how long is it until purchasing power is cut in half?