Homework Sourse1 Suppose that your annual salary today is 52000 and increas
1) Suppose that your annual salary today is $52,000 and increases at the same rate as inflation [continuous compounding]. If inflation continues at an annual rate of 6%, how long will it be before $52,000 increases to an annual salary of a million dollars?
2) Suppose that a gallon of milk costs $4 today and that a dozen eggs costs $1.50. Assume that the price of milk increases at a rate of 2% each year and that the price of eggs increases at a rate of 3% each year. If the inflation rates of these items do not change, how much will each of these items cost in 10, 20, 30, 40, and 50 years?
3) Create a chart and graph to show the change in price over time. [You could use Excel.]
What if the price of a dozen eggs increases at an annual rate of 6%?
What is your observation?
1) Suppose that your annual salary today is $52,000 and increases at the same rate as inflation [continuous compounding]. If inflation continues at an annual rate of 6%, how long will it be before $52,000 increases to an annual salary of a million dollars?
2) Suppose that a gallon of milk costs $4 today and that a dozen eggs costs $1.50. Assume that the price of milk increases at a rate of 2% each year and that the price of eggs increases at a rate of 3% each year. If the inflation rates of these items do not change, how much will each of these items cost in 10, 20, 30, 40, and 50 years?
3) Create a chart and graph to show the change in price over time. [You could use Excel.]
What if the price of a dozen eggs increases at an annual rate of 6%?
What is your observation?
1) Suppose that your annual salary today is $52,000 and increases at the same rate as inflation [continuous compounding]. If inflation continues at an annual rate of 6%, how long will it be before $52,000 increases to an annual salary of a million dollars?
2) Suppose that a gallon of milk costs $4 today and that a dozen eggs costs $1.50. Assume that the price of milk increases at a rate of 2% each year and that the price of eggs increases at a rate of 3% each year. If the inflation rates of these items do not change, how much will each of these items cost in 10, 20, 30, 40, and 50 years?
3) Create a chart and graph to show the change in price over time. [You could use Excel.]
What if the price of a dozen eggs increases at an annual rate of 6%?
What is your observation?
Solution
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| Annual salary Today (P) | = | 52000 | $ | |
| Rate Of Inflation \'r | = | 6% | ||
| Final Amount | = | 1000000 | $ | |
| Amount | = | P (1 + r/100 )^n | ||
| 1000000 | = | 52000(1.06)^n | ||
| 19.23076923 | = | 1.06^n | ||
| Taking natural log both sides | ||||
| ln (19.23) | = | n * ln(1.06) | ||
| 2.95651156 | = | n * ln(1.06) | ||
| n | = | 50.73909321 | years |
![1) Suppose that your annual salary today is $52,000 and increases at the same rate as inflation [continuous compounding]. If inflation continues at an annual r](/WebImages/32/1-suppose-that-your-annual-salary-today-is-52000-and-increas-1094027-1761576534-0.webp "1) Suppose that your annual salary today is $52,000 and increases at the same rate as inflation [continuous compounding]. If inflation continues at an annual r")
