5. Interest, inflation, and purchasing power
Suppose Kyoko is an avid reader and buys only mystery novels. Kyoko deposits $3,000 in a bank account that pays an annual nominal interest rate of 10%. Assume this interest rate is fixed—that is, it won't change over time. At the time of her deposit, a mystery novel is priced at $15.00.
Initially, the purchasing power of Kyoko's $3,000 deposit is___________mystery novels.
For each of the annual inflation rates given in the following table, first determine the new price of a mystery novel, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Kyoko'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 mystery novel. For example, if you find that the deposit will cover 20.7 mystery novels, you would round the purchasing power down to 20 mystery novels under the assumption that Kyoko will not buy seven-tenths of a mystery novel.
|
Annual Inflation Rate |
|||
|---|---|---|---|
| 0% | 10% | 13% | |
| Number of Novels Kyoko Can Purchase after One Year | |||
| Real Interest Rate | |||
When the rate of inflation is equal to the interest rate on Kyoko's deposit, the purchasing power of her deposit ______ over the course of the year.
1) Purchasing power = 3000/15 = 200 novels
2) Annual inflation rate is 0%:
Price of novel = $ 15
No. of novels purchased = 3300/15 = 220 novels
Real interest rate = Nominal interest rate - Inflation = 10% - 0 = 10%
Annual inflation rate is 10%:
Price of novel = $ 15 + 10% of 15 = 15 + 1.5 = 16.5
No. of novels purchased = 3300/16.5 = 200 novels
Real interest rate = Nominal interest rate - Inflation = 10% - 10% = 0%
Annual inflation rate is 13%:
Price of novel = $ 15 + 13% of 15 = 15 + 1.95 = 16.95
No. of novels purchased = 3300/16.95 = 194.69 = 195 novels
Real interest rate = Nominal interest rate - Inflation = 10% - 13% = - 3%
3) remains same over the course of year
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