Question

  aplia ch 11   

5. Interest, inflation, and purchasing power Suppose Valerie is a sports fan and buys only baseball caps. Valerie 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 Valerie'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 Valerie'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 Valerie will not buy seven-tenths of a baseball cap. Annual Inflation Rate (FILL IN BLANKS BELOW) 0% 5% 8% Number of Caps Valerie Can Purchase after One Year ________ ________ ________ Real Interest Rate When the rate of inflation is less than the interest rate on Valerie's deposit, the purchasing power of her deposit over the course of the year.

Answer 1

Initially with $3,000, Valerie can purchase $3,000 / $10 = 300 caps.

1) When inflation rate is 0%:

Number of Caps Valerie Can Purchase after One Year: [$3,000 * (1.05)] / $10 = 315 caps

Real interest rate = [[1 + nominal interest rate] / [1 + inflation rate]] - 1

Real interest rate = [1.05] / 1 = 5%

2) When inflation rate is 5%:

Number of Caps Valerie Can Purchase after One Year: Value of investment after a year / price of cap after a year = [$3,000 * (1.05)] / [$10 * 1.05] = 300 caps

Real interest rate = [[1 + nominal interest rate] / [1 + inflation rate]] - 1

Real interest rate = [[1.05] / [1.05]] = 0%

3) When inflation rate is 8%:

Number of Caps Valerie Can Purchase after One Year: Value of investment after a year / price of cap after a year = [$3,000 * (1.05)] / [$10 * 1.08] = 291.67 caps or 291 caps

Real interest rate = [[1 + nominal interest rate] / [1 + inflation rate]] - 1

Real interest rate = [[1.05] / [1.08]] 1 = -2.78%

Annual inflation rate	0%	5%	8%
Number of Caps	315	300	291
Real Interest Rate	5%	0%	-2.78%

When the inflation rate is 0%, that is less than the interest rate of 5% on Valenie's deposit her purchasing power increases over time. She initially can buy 300 caps while after 1 year her wealth can buy 315 caps with the money deposited.

Therefore, when the rate of inflation is less than the interest rate on Valenie's deposit her purchasing power rises overtime.