Suppose Susan is a sports fan and buys only baseball caps. Susan deposits $2,000

Question

Suppose Susan is a sports fan and buys only baseball caps. Susan 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 Susan's $2,000 deposit is100 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 Susan'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 Susan will not buy seven-tenths of a baseball cap. Annual Inflation Rate 15% 100 090 18% Number of Caps Susan Can Purchase after One Year Real Interest Rate over the When the rate of inflation is equal to the interest rate on Susan's deposit, the purchasing power of her deposit course of the year.

Explanation / Answer

Initially, the purchasing power of Susan's $2000 deposit is 100 baseball caps (=2000/20)

Amount in the bank account after 1 year = 2000 x 1.15 = $2300

Price of baseball cap = (1 + inflation rate) x Present Price

Real interest rate = Nominal interest rate - Inflation rate

Number of caps = Amount after 1 year/Price of baseball cap

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

Annual Inflation rate 0% 15% 18% Price of baseball cap 20 23 23.6 Number of caps Susan can purchase after 1 year 115 100 97 Real interest rate 15.00% 0.00% -3.00%

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