Chapter 7.8, Problem 7PPS

a.

To determine

To find: The effective monthly inflation rate in Austria in $1922$ .

Answer to Problem 7PPS

Effective monthly inflation rate was $25.496\%$ .

Explanation of Solution

Given Information: Inflation rate for one year was $1426\%$ .

Calculation:

  $\begin{array}{l}$ AnnualEffectiveRate={(1+\frac{ANR}{12})}^{12}-1$$ 14.26={(1+\frac{ANR}{12})}^{12}-1$\sqrt[12]{15.26}=1+\frac{ANR}{12}\\ 1.25495902=1+\frac{ANR}{12}\\ EffectiveMonthlyRate=\frac{ANR}{12}=0.25495902\\ EffectiveMonthlyRate\approx 25.496\%\end{array}$

Thus, the effective monthly inflation rate was $25.496\%$ .

b.

To determine

To find: The increase in cost of an item in a span of $3$ months.

Answer to Problem 7PPS

The final cost would have been near about $19.764$ crowns.

Explanation of Solution

Given Information: Item’s initial cost was

  $10$ crowns.

Calculation:

The effective monthly inflation rate was $25.496\%$ .

Function representing the final cost is,

  $A(m)=P{(1.25496)}^m$ ( where $m$ represents number of months)

  $\begin{array}{l}$ A(3)=10{(1.25496)}^3$A(3)\approx 10(1.97647)\\ A(3)\approx 19.764\end{array}$

Thus, the final cost would have been near about $19.764$ crowns.