3. In class we have shown the formula for the present value of a growing perpetuity. The formula can be used to evaluate the present value of a growing annuity. The following question will get you through the calculation. You have been offered a job at $100,000 a year. Your first salary will be paid in a year. You expect your salary to increase by 4% a year until you retire in 20 years. Given an interest rate of 6% a year, what is the present value of your salary? Note: The idea is to calculate the present value of your salary stream as if you were to live forever and then subtract from it the present value of the stream of salaries from year 21 onward. Follow these steps in your calculation: Step 1: calculate the present value of your salary stream assuming that you were to live forever (hint: use the growing perpetuity formula). Step 2: Suppose that you are in year 20. Calculate the present value of the stream of salaries which starts in year 21 and continues forever. (Hint: first calculate the salary in year 21. What is the growth rate of this stream of salaries?). Step 3: discount back the value that you calculated in step 2 to year 0. Subtract the value from in step 3 from the value that you got in step 1. This is the value of your growing annuity Compare your result to the one you'd get if you used the formula in the book. 3. In class we have shown the formula for the present value of a growing perpetuity. The formula can be used to evaluate the present value of a growing annuity. The following question will get you through the calculation. You have been offered a job at $100,000 a year. Your first salary will be paid in a year. You expect your salary to increase by 4% a year until you retire in 20 years. Given an interest rate of 6% a year, what is the present value of your salary? Note: The idea is to calculate the present value of your salary stream as if you were to live forever and then subtract from it the present value of the stream of salaries from year 21 onward. Follow these steps in your calculation: Step 1: calculate the present value of your salary stream assuming that you were to live forever (hint: use the growing perpetuity formula). Step 2: Suppose that you are in year 20. Calculate the present value of the stream of salaries which starts in year 21 and continues forever. (Hint: first calculate the salary in year 21. What is the growth rate of this stream of salaries?). Step 3: discount back the value that you calculated in step 2 to year 0. Subtract the value from in step 3 from the value that you got in step 1. This is the value of your growing annuity Compare your result to the one you'd get if you used the formula in the book