1. When Joe started his job at the laundromat 5 years ago, his wage was $5.50 an hour. Today his wage is $8.50 an hour. If Joe started his job in the base year, and his real wage is the same as when he started, what is the Consumer Price Index today?
2. The International Disc Jockey\'s Union has a wage contract that stipulates a yearly wage increase based on the Consumer Price Index. If this year\'s wage is $25.00, the current CPI is 180, and the contract was first signed in the base year, what was the original salary the first year of the contract?
3. Shelby bought her dream car, a 1966 red convertible Mustang, with a loan from her credit union. If Shelby paid 5.7% and the bank earned a real rate of return of 4.7%, what was the inflation rate over the life of the loan?
4. Tim is feeling magnanimous, and decides to loan his mother enough for her to pay off her credit card bills. If Tim wants to earn 3.3% and expects inflation to be 4.3%, how much will he charge his mother for the loan?
thanks
for question 2 why divide 100/150
1. Ah, the good ole' laundromat wage! Let's solve this math puzzle, shall we? Joe's real wage is the same as when he started, which means his wage has kept up with inflation. To find the Consumer Price Index (CPI) today, we can use the formula Real Wage = Nominal Wage / CPI. Plugging in the given values, his starting wage was $5.50, and his current wage is $8.50. Since the real wage is the same, we have $5.50 / CPI = $8.50. Solving for CPI, we find CPI ≈ $5.50 / $8.50, which is approximately 0.647. So, the Consumer Price Index today is around 0.647. (Psst, make sure you double-check your calculations!)
2. Ah, the glamorous life of a disc jockey! Now, let's find the original salary of the first year of the contract. The wage increase is based on the Consumer Price Index (CPI). We know the current CPI is 180 and this year's wage is $25.00. So, we can set up the equation: Original Salary / CPI = Current Salary. Plugging in the values, we have Original Salary / 180 = $25.00. Solving for Original Salary, we find Original Salary ≈ 180 × $25.00. That gives us the original salary of the first year of the contract. Dance on, DJ!
3. Ah, Shelby and her dream car! Let's calculate the inflation rate over the life of her loan, shall we? Shelby paid 5.7% interest on her loan, while the bank had a real rate of return of 4.7%. Now, we know that the inflation rate can be calculated by subtracting the real rate of return from the nominal rate. So, the inflation rate over the life of the loan is approximately 5.7% - 4.7% = 1%. There you have it, Shelby's journey through the world of inflation!
4. Ah, Tim the benefactor! Let's determine how much he'll charge his dear mother for the loan, shall we? Tim wants to earn 3.3% on the loan, and he expects inflation to be 4.3%. To calculate the loan charge, we need to add the expected inflation rate to Tim's desired interest rate. So, the loan charge will be 3.3% + 4.3% = 7.6%. Tim will charge his mother 7.6% interest on the loan. Ah, what son wouldn't go the extra mile for their mom's credit card bills?
1. To find the Consumer Price Index (CPI) today, we need to compare Joe's initial wage to his current wage and adjust for inflation. Let's calculate the inflation rate first.
Inflation rate = (Current wage - Initial wage) / Initial wage
Inflation rate = ($8.50 - $5.50) / $5.50
Inflation rate = $3.00 / $5.50
Now, let's calculate the CPI. CPI is a measure of the average change over time in the prices paid by consumers for a market basket of goods and services. We can use the inflation rate to find the CPI today.
CPI = 1 + Inflation rate
CPI = 1 + ($3.00 / $5.50)
2. To find the original salary in the first year of the contract, we can use the CPI and the current wage.
Original salary = Current wage / CPI
Original salary = $25.00 / 180
3. To find the inflation rate over the life of the loan, we need to compare the bank's real rate of return with the interest rate Shelby paid. The difference between the two rates is the inflation rate.
Inflation rate = Bank's real rate of return - Shelby's interest rate
Inflation rate = 4.7% - 5.7%
4. To calculate how much Tim should charge his mother for the loan, we can use the nominal interest rate and subtract the expected inflation rate.
Loan interest rate = Nominal interest rate - Expected inflation rate
Loan interest rate = 3.3% - 4.3%
#1) (8.5 / 4) x 100 = 212.5
#2) (100 / 150) x 25 = 16.67
#3) 5.7-4.7 = 1
#4) 3.3 + 4.3 = 7.6