Question

5. Interest, inflation, and purchasing power

Suppose Eileen is a sports fan and buys only baseball caps. Eileen deposits $3,000 in a bank account that pays an annual nominal interest rate of 15%. 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 $15.00.

Initially, the purchasing power of Eileen'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 Eileen'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 Eileen will not buy seven-tenths of a baseball cap.

	Annual Inflation Rate
	0%	15%	18%
Number of Caps Eileen Can Purchase after One Year
Real Interest Rate

When the rate of inflation is equal to the interest rate on Eileen's deposit, the purchasing power of her deposit __rises, falls or remains the same__________ over the course of the year.

Answer 1

Initially, the purchasing power of Eileen's $3,000 deposit is Initial deposit/price = 3000/15 =200 baseball caps.

	0%	15%	18%
Number of comics	230	200	195
Real interest rate	15%	0%	-3%

a) When inflation is 0%, the price will remain same at $15

Value of deposit = 3000x(1+0.15) = 3450

Purchasing power = 3450/15=230

Real interest rate = Nominal-inflation = 15-0=15%

b) When the inflation is 15% the price increases to 15x(1+0.15) = 17.25

Purchasing power = 3450/17.25 = 200

Real interest rate = 15-15=0%

c) When the inflation is 18%,the price increases to 15x(1+0.18)=17.7

Purchasing power = 3450/17.7 =194.9 or 195

Real interest rate = 15-18=-3%

When the rate of inflation is equal to the interest rate on Eileen's deposit, the purchasing power of her deposit remains the same over the course of the year.