5. Interest, inflation, and purchasing power Suppose Ana is a sports fan and buy

Question

5. Interest, inflation, and purchasing power Suppose Ana is a sports fan and buys only baseball 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 caps, Ana deposits $3,000 in a bank account that pays an annual nominal interest rate of 15%. at $15.00. iiall,the purchasing power of Ana's $3,000 deposit ibsball caps. rises at the rate of For each of the annual inflation rates given in the following table, first determine the new price of a baseball cap, assuming it inflation. Then enter the corresponding purchasing power of Ana's deposit after one year in the first row of enter the value for the real interest rate at each of the given inflation rates. the table for each inflation rate. Finally, Hint: 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 Ana will not buy seven-tenths of a baseball cap. Annual Inflation Rate 15% 0% 18% Number of Caps Ana Can Purchase after One Year Real Interest Rate When the rate of inflation is less than the interest rate on Ana's deposit, the purchasing power of her deposit of the year. over the course

Explanation / Answer

ANSWER:

1) initially ana can purchase 200 caps as ana deposit / price of 1 baseball cap that is $3000 / $15 = 200

2) a) when inflation is 0% then real rate is equal to nominal rate.

nominal rate = real rate + inflation rate

15% = real rate + 0%

real rate = 15% - 0% = 15%

future value of $3,000 deposit at 15% real rate = deposit(f/p,i,n)

fv = 3,000(f/p,15%,1) = 3,000 * 1.15 = $3,450

no of baseball cpas that ana can buy = fv / price of base ball cap = $3,450 / $15 = 230

b) when inflation rate is 15%

nominal rate = real rate + inflation rate

15% = real rate + 15%)

15% = real rate + 15%

15% - 15% = real rate

0% = real rate

future value of $3,000 deposit at 0% real rate = deposit(f/p,i,n)

fv = 3,000(f/p,0%,1) = 3,000 * 1 = $3,000

no of baseball cpas that ana can buy = fv / price of base ball cap = $3,000 / $15 = 200

c) when inflation rate is 18%

nominal rate = real rate + inflation rate

15% = real rate + 18%

real rate = 15% - 18% = -3%

future value of $3,000 deposit at -3% real rate = deposit(f/p,i,n)

fv = 3,000(f/p,-3%,1) = 3,000 * 1 = $3,000 * - 1.03 = $2,910

no of baseball cpas that ana can buy = fv / price of base ball cap = $2,910 / $15 = 194

3) rises as seen from above.

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