Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 316

When your cash balances are at present \(\$ 1,000\) and inflation is expected to be \(12 \%\) per year, what will be your real balances after 4 years in terms of current prices?

Short Answer

Expert verified
The real cash balance after 4 years, adjusted for a 12% annual inflation rate, will be \(\$1,000\) in terms of current prices.

Step by step solution

01

Identify the given information

We are given the following information: - Initial cash balance: \(P_0 = \$ 1,000\) - Inflation rate: \(r = 12 \% = 0.12\) - Time period: \(t = 4\) years.
02

Calculate the inflated nominal cash balance after 4 years

To calculate the nominal cash balance after 4 years, we need to account for the inflation rate. We can use the formula for calculating future value with an annual increase: \(P_t = P_0 (1 + r)^t\) where: - \(P_t\) is the nominal cash balance after \(t\) years - \(P_0\) is the initial cash balance - \(r\) is the annual inflation rate as a decimal - \(t\) is the time period in years. Plugging in the given values, we have: \(P_t = 1,000 (1 + 0.12)^4\)
03

Calculate the real cash balance after 4 years

Now, we want to find the real cash balance adjusted for inflation. To do this, we need to divide the nominal cash balance by the inflated value for the given time period. We can use the same formula as above to calculate the inflated value: \(V_t = (1 + r)^t\) Dividing the nominal cash balance by the inflated value, we get: \(Real\_balance_t = \frac{P_t}{V_t}\) Substituting the values, we get: \(Real\_balance_t = \frac{1,000(1 + 0.12)^4}{(1 + 0.12)^4}\) Since the denominator is equal to the nominal cash balance's inflating factor \((1+0.12)^4\), they will cancel out when dividing: \(Real\_balance_t = \$1,000\)
04

State the final answer

After 4 years, the real cash balance adjusted for inflation will be \(\$1,000\) in terms of today's prices.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose the government has decided to combat inflation by raising taxes on disposable income. What specific type of inflation would this be used against?

Assume there are only 5 kinds of labor in the economy, engineers, secretaries, truckers, steel workers and farm workers. It is impossible to move from one category to another without Several years .of training. Suppose that in each category there are \(1,000,000\) people unemployed (thus in total there are \(5,000,000\) people unemployed), and each increase of \(\$ 1\) billion in GNP causes an increase of 20,000 in the demand for engineers, 30,000 for secretaries, 25,000 for truckers, 15,000 for steel workers, and 5,000 in the demand for farm workers. 1) By how much must GNP be increased to remove all unemployment? 2) If GNP is increased to remove all unemployment, from which source would you anticipate inflationary pressure?

When can a government budget deficit be considered to be neutral with respect to monetary factors? Explain.

What are some of the undesirable effects of inflation?

How can the Automatic Monetary Policy of a fixed growth rate in the Money Supply as proposed by Milton Friedman, have a stabilizing effect on the economy?
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free