Suppose Ana Is A Cinephile And Buys Only Movie Tickets

Suppose Ana is a cinephile and buys only movie tickets. Ana deposits

Suppose Ana is a cinephile and buys only movie tickets. Ana deposits $3,000 in a bank account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed—that is, it won't change over time. At the time of her deposit, a movie ticket is priced at $10.00. Initially, the purchasing power of Ana's $3,000 deposit is ___________movie tickets.

For each of the annual inflation rates given in the following table, first determine the new price of a movie ticket, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Ana's deposit after one year in the first row of the table for each inflation rate. Finally, enter the value for the real interest rate at each of the given inflation rates. Hint: Round your answers in the first row down to the nearest movie ticket. For example, if you find that the deposit will cover 20.7 movie tickets, you would round the purchasing power down to 20 movie tickets under the assumption that Ana will not buy seven-tenths of a movie ticket. Annual Inflation Rate 0% 5% 8% # of tickets she can purchase after 1 year _____ _____ ______ Real interest rate ____ ____ _____ When the rate of inflation is less than the interest rate on Ana's deposit, the purchasing power of her deposit (remains the same/falls/rises) over the course of the year.

Paper For Above instruction

The scenario involving Ana, a cinephile who invests $3,000 in a bank account with a fixed nominal interest rate of 5%, illustrates fundamental concepts in inflation, real interest rates, and purchasing power. The problem begins with calculating Ana's initial purchasing power in terms of movie tickets, followed by examining how different inflation rates impact her ability to buy movie tickets after one year.

Initially, Ana's deposit of $3,000, with a ticket price of $10, provides her with the capacity to buy 300 movie tickets ($3,000 / $10). This initial measurement sets her baseline purchasing power before any inflation or interest effects are considered.

When analyzing the effects of inflation, the new price of a movie ticket after one year depends on the inflation rate. For a 0% inflation rate, the ticket price remains at $10, and Ana's purchasing power stays at 300 tickets. However, as inflation increases to 5% and 8%, the ticket prices adjust accordingly. After accounting for inflation, the new price of a ticket becomes:

• $10 × (1 + inflation rate)

Thus, at 5% inflation, the ticket price becomes $10.50, and at 8% inflation, it becomes $10.80.

To find the number of tickets Ana can purchase after one year, her accumulated deposit must be adjusted for real value. The nominal interest accrued over a year on her deposit is:

• $3,000 × 5% = $150

Therefore, the total amount in her account after one year is:

• $3,000 + $150 = $3,150

However, inflation affects the real value of her money. The real value of her deposit—what it can buy in terms of movie tickets—depends on both the nominal interest rate and the actual inflation rate.

The number of tickets she can buy after one year at each inflation scenario is calculated by dividing her deposit's real value by the new ticket price. The real value of her deposit, in terms of current dollars, is adjusted for inflation. The purchasing power of her deposit in tickets can be approximated as:

• (Deposit after interest) / (New ticket price)

Calculations for each inflation rate:

At 0% inflation:

Ticket price remains at $10.00, and she can buy:

• 3000 × (1 + 0.05) = $3,150 total deposit after interest.
• Number of tickets: $3,150 / $10 = 315 tickets.

At 5% inflation:

Ticket price: $10 × (1 + 0.05) = $10.50

Deposit after interest: $3,150

Number of tickets: floor($3,150 / $10.50) = floor(300) ≈ 300 tickets (rounded down)

At 8% inflation:

Ticket price: $10 × (1 + 0.08) = $10.80

Deposit after interest: $3,150

Number of tickets: floor($3,150 / $10.80) ≈ floor(291.67) = 291 tickets (rounded down)

The real interest rate, which reflects the growth of purchasing power adjusted for inflation, is calculated as:

• Real interest rate = Nominal interest rate - Inflation rate

Accordingly:

• At 0% inflation: 5% - 0% = 5%
• At 5% inflation: 5% - 5% = 0%
• At 8% inflation: 5% - 8% = -3%

When the inflation rate is less than the nominal interest rate, the purchasing power of Ana's deposit increases or remains stable. Specifically, if inflation is below the nominal interest rate, her deposit's real value increases over the year, allowing her to buy more or the same number of movie tickets at year's end.

Summary Table

In conclusion, when the inflation rate is less than the interest rate on Ana's deposit, the purchasing power of her money (remains the same or) rises over the course of the year. This is because the real value of her deposits grows, allowing her to buy more movie tickets than she could initially, even after accounting for inflation.

References

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