Question

Suppose Janet is an avid reader and buys only mystery novels. Janet deposits $4,000 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 mystery novel is priced at$10.00. Initially, the purchasing power of Janet's $4,000 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 Janet'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 Janet will not buy seven-tenths of a mystery novel Annual Inflation Rate 0% 5% 890 Number of Novels Janet Can Purchase after One Year Real Interest Rate When the rate of inflation is greater than the interest rate on Janet's deposit, the purchasing power of her deposit ▼ over the course of the year.

Answer 1

Answer@@@@

Initial deposit of Kate = $4,000

Price of one novel = $10

Purchasing power of $4,000 deposit = Deposit/Price of one novel = $4,000/$10 = 400 novels

Thus, the purchasing power of Kate's $4,000 deposit is 400 mystery novels.

CASE I - Inflation rate is 0%

Current price of novel - $10

Price of novel after one year = Current price of novel + (Current price of novel * Inflation rate)

                                         = $10 + ($10 * 0) = $10

Current value of deposit = $4,000

Interest rate on deposit = 5% or 0.05

Value of deposit after one year = Current value of deposit + (Current value of deposit * interest rate)

   = $4,000 + ($4,000 * 0.05) = $4,000 + $200 = $4,200

Calculate Number of novels purchased after one year -

Novels purchased = Value of deposit after one year/Price of novel after one year

                          = $4,200/10 = 420 novels

Calculate real interest rate -

Real interest rate = Nominal interest rate - Inflation = 5% - 0% = 5%

CASE II - Inflation rate is 5%

Current price of novel - $10

Price of novel after one year = Current price of novel + (Current price of novel * Inflation rate)

                                         = $10 + ($10 * 0.05) = $10.50

Current value of deposit = $4,000

Interest rate on deposit = 5% or 0.05

Value of deposit after one year = Current value of deposit + (Current value of deposit * interest rate)

   = $4,000 + ($4,000 * 0.05) = $4,000 + $200 = $4,200

Calculate Number of novels purchased after one year -

Novels purchased = Value of deposit after one year/Price of novel after one year

                          = $4,200/10.50 = 400 novels

Calculate real interest rate -

Real interest rate = Nominal interest rate - Inflation = 5% - 5% = 0%

CASE III - Inflation rate is 8%

Current price of novel - $10

Price of novel after one year = Current price of novel + (Current price of novel * Inflation rate)

                                         = $10 + ($10 * 0.08) = $10.80

Current value of deposit = $4,000

Interest rate on deposit = 5% or 0.05

Value of deposit after one year = Current value of deposit + (Current value of deposit * interest rate)

   = $4,000 + ($4,000 * 0.05) = $4,000 + $200 = $4,200

Calculate Number of novels purchased after one year -

Novels purchased = Value of deposit after one year/Price of novel after one year

                          = $4,200/10.80 = 388 novels

Calculate real interest rate -

Real interest rate = Nominal interest rate - Inflation = 5% - 8% = -3%

Following is the required graph -