Interest, inflation, and purchasing power
Suppose Eileen is a sports fan and buys only baseball caps. Eileen deposits $2,000 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 $20.00.
Initially, the purchasing power of Eileen's $2,000 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 Annual Inflation Rate Annual Inflation Rate
0% 15% 18%
Number of Caps Eileen Can Purchase after One Year Real Interest Rate When the rate of inflation is less than the interest rate on Eileen's deposit, the purchasing power of her deposit _____ over the course of the year.
Nominal and real income or purchasing power
The real income and real interest are affected by the rate of inflation.
Eileen's initial income (deposit) was $2,000
Price per cap was $20.
Hence her initial purchasing power = (Income/Price) = $2,000/$20 = 20 caps.
AFTER ONE YEAR
Income will be 15% more because of deposit interest. New income = (1.15)($2,000) = $2,300.
New price of cap due to 15% inflation rate = ($20)(1.15) = $23.
Purchasing power after 1 year = $2,300/$23 = 100 caps.
There is NO change in purchasing power after one year.
The real interest rate after one year, adjusted for 15% inflation, r = (1.+ nominal rate)/( 1 + inflation rate) (nominal rate
Real interest = (1.15/1.15)(0.15) = 0.15 or 15%. The nominal and real rates are the same because the interest rate offsets the inflation rate and each is 15%.