Question

Interest, inflation, and purchasing power Suppose Maria is an avid reader and buys only comic books.

Maria deposits $3,000 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 comic
book is priced at $15.00. Initially, the purchasing power of Maria's $3,000 deposit is comic books,
For each of the annual inflation rates given in the following table,
first determine the new price of a
comic book, assuming it rises at the rate of inflation. Then enter the corresponding purchasing
power of Maria'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 comic book. For example, if you find that the
deposit will cover 20.7 comic books, you would round the purchasing power down to 20 comic
books under the assumption that Maria will not buy seven-tenths of a comic book. Annual Inflation Rate 0% 10% 13% Number of Comics Maria Can Purchase after One Year Real Interest Rate over the When the rate of inflation is greater than the interest rate on
Maria's deposit, the purchasing power of her deposit course of the year ?

Answer 1

Maria's $3,000 deposit allows her to initially purchase 200 comic books. With a 0% inflation rate, her purchasing power remains the same, but a 10% inflation rate diminishes it to the purchase of 200 comics with a real interest rate of 0%, and a 13% inflation rate further reduces her purchasing power to 194 comics with a real interest rate of -3%.

Step-by-step explanation:

Maria's initial deposit of $3,000 allows her to purchase 200 comic books, priced at $15 each. When the inflation rate is 0%, the price of comic books does not change, so she can still purchase 200 comic books after one year. The real interest rate in this case remains at 10%, as there is no inflation to lower the purchasing power.

With a 10% inflation rate, the price of each comic book would rise to $16.50. Maria's deposit will grow to $3,300 due to the interest, yet her purchasing power decreases as she can now purchase only 200 comic books (since partial comic books are not considered). The real interest rate is 0% when inflation is 10%, as it offsets the nominal interest rate.

When the inflation rate is 13%, the price of a comic book increases to $16.95. Maria's deposit would still grow to $3,300, but she could only buy roughly 194 comic books, and her purchasing power would be rounded down to 194 comics. The real interest rate here becomes negative, specifically -3%, as the inflation rate surpasses the nominal interest rate, effectively eroding her purchasing power over the course of the year.