Question

5. Interest, inflation, and purchasing power 

Suppose Megan is a sports fan and buys only baseball caps. Megan 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 baseball cap is priced at $10.00. 

Initially, the purchasing power of Megan's $3,000 deposit is _______  baseball caps. 

For each of the annual inflation rates given in the following table, first determine the new price of a baseball cap, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Megan'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 baseball cap. For example, if you find that the deposit will cover 20.7 baseball caps, you would round the purchasing power down to 20 baseball caps under the assumption that Megan will not buy seven-tenths of a baseball cap. 

When the rate of inflation is greater than the interest rate on Megan's deposit, the purchasing power of her deposit _______  over the course of the year.

Answer 1

Purchasing power = Initial Deposit/Price

Initial deposit= $3,000

Price of baseball caps= $10

Initially the purchasing power is $3,000/$10=300 baseball caps

Annual Inflation Rate

                                                                                                                               0%                   5%              8%

Number of baseball caps Megan can purchase after one year 315                200                195

Real Interest rate 5%                   0%                -3%

When annual inflation rate is 0%

Real interest rate= Nominal rate – inflation rate

Nominal rate is 5%

Real interest rate= 5%-0%=5%

After one year Meghan’s deposit will be $3000 (1+.05)=$3,150

Price of baseball caps when inflation is 0%= $10

Meghan can purchase = $3150/$10=315 baseball caps.

When annual inflation rate is 5%

Price of baseball cap will be $10 x.05=$10.50

Meghan can purchase = $3,150/$10.50=300 baseball caps.

Real interest rate= 5%-5%=0%.

When annual inflation rate is 8%

Price of baseball caps will be $10 x.08=$10.80

Meghan can purchase = $3,150/$10.80=291 baseball caps

Real interest rate= 5%-8%=-3%.

Falls.