Suppose Terese is a sports fan and buys only baseball caps. Terese deposits $2,0
ID: 1228175 • Letter: S
Question
Suppose Terese is a sports fan and buys only baseball caps. Terese deposits $2,000 in a bank account that pays an annual interest rate of 10%. You can assume that 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 Terese's $2,000 deposit is baseball caps. The price of a baseball cap rises at the rate of inflation. For each of the annual inflation rates in the following table, select the corresponding purchasing power of Terese's deposit after one year, and enter the value for the real interest Round your answers 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 Terese will not buy seven-tenths of a baseball cap. When the rate of inflation is less than the interest rate on Terese's deposit, the purchasing power of her deposit_over the course of the year.Explanation / Answer
Given the price of cap is currently at $10 per cap and the initial value of the deposit is $2000. So with this purchasing power value, the number of caps that can be purchased is 2000/10 = 200 caps.
When the price of caps rises with inflation, it becomes $10 with 0% inflation, $11 with 10% inflation and $12 with 20% inflation.
Because the deposits have a fixed 10% interest rate, it will become $2200 after 1 year.
Case 1: inflation is 0%.
In this case, nothing changes. Price of caps is still $10 and deposits are $2200. So the number of caps that can be purchased is 2200/10 = 220 caps
Case 2: inflation is 10%.
In this case, the price of cap changes. Price of caps becomes $11 and deposits are $2200. So the number of caps that can be purchased is 2200/11 = 200 caps
Case 1: inflation is 20%.
In this case, the price of caps changes. Price of caps is $12 and deposits are $2200. So the number of caps that can be purchased is 2200/12 = 183 caps
Comparing the number of caps before and after one year, we see that when the inflation rate is 0%, real interest rate is [(220-200)/200]*100 = 10%. When the inflation rate is 10%, real interest rate is [(200-200)/200]*100 = 0%. When the inflation rate is 20%, real interest rate is [(183-200)/200]*100 = -8.5%.
Inflation
Price of cap
Deposit value
Number of caps after one year
Original number of caps
Real interest rate
0
10
2200
220
200
10
10
11
2200
200
200
0
20
12
2200
183
200
-8.5
Inflation
Price of cap
Deposit value
Number of caps after one year
Original number of caps
Real interest rate
0
10
2200
220
200
10
10
11
2200
200
200
0
20
12
2200
183
200
-8.5
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