Question

Suppose Valerie is an avid reader and buys only mystery novels. Valerie deposits $2,000 in a bank account that pays an annual nominal interest rate of 10%. Assume this interest rate is fixed—that is, it won't change over time. At the time of her deposit, a mystery novel is priced at $10.00. Initially, the purchasing power of Valerie's $2,000 deposit is______mystery novels.

For each of the annual inflation rates given in the following table, first determine the new price of a mystery novel, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Valerie'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.
Annual Inflation Rate Annual Inflation Rate Annual Inflation Rate
0% 10% 13%
Number of Novels
Valerie Can Purchase
after One Year
Real Interest Rate
When the rate of inflation is equal to the interest rate on Valerie's deposit, the purchasing power of her deposit_____course of the year.

Answer 1

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Step-by-step explanation:

Answer 2

Valerie's initial purchasing power is 200 novels, but it decreases with inflation while the real interest rate falls proportionally.

How is that so?

Given:

• Initial deposit = $2,000
• Price of a mystery novel = $10.00

Calculation:

Initial purchasing power = Initial deposit / Price of a novel = $2,000 / $10.00 = 200 mystery novels

Purchasing Power after One Year

For each inflation rate, we need to:

• Calculate the new price of a mystery novel after inflation.
• Calculate the new purchasing power of Valerie's deposit after one year.
• Calculate the real interest rate.

Inflation Rate = 0%

New Price: $10.00 * (1 + 0%) = $10.00

Purchasing Power: $2,200 / $10.00 = 220 mystery novels

Real Interest Rate: 10% - 0% = 10%

Inflation Rate = 10%

New Price: $10.00 * (1 + 10%) = $11.00

Purchasing Power: $2,200 / $11.00 = 200 mystery novels

Real Interest Rate: 10% - 10% = 0%

Inflation Rate = 13%

New Price: $10.00 * (1 + 13%) = $11.30

Purchasing Power: $2,260 / $11.30 = 194.69 mystery novels

Real Interest Rate: 10% - 13% = -3%

As the inflation rate increases, the real interest rate decreases. This means that the purchasing power of Valerie's deposit declines even though it is earning interest.