You have been offered a job with an unusual bonus structure. As long as you stay with the​ firm, you will get an extra $ 68 comma 000$68,000 every 77 ​years, starting 77 years from now. What is the present value of this incentive if you plan to work for the company for 4242 years and the interest rate is 5 %5% ​(EAR)? ​(Note​: Be careful not to round any intermediate steps less than six decimal​ places.) 


To calculate the present value (PV) of the bonus structure, we need to account for the fact that these bonuses occur at regular intervals in the future, making this a case of discounted future payments.

Given:
- The bonus amount $ B = 68,000 $ USD.
- The time between bonuses is 77 years.
- You plan to work for 42 years.
- The interest rate is $ r = 5\% $ EAR (Effective Annual Rate).

### Steps:
1. **Determine the number of bonuses**: Since the bonuses are paid every 7 years, we need to know how many bonuses you'll receive over 42 years. This is calculated as:

   \[
   N = \frac{42}{7} = 6 \text{ bonuses}.
   \]

2. **Calculate the present value of each bonus**: For each bonus payment, the present value is given by the formula for discounting a future payment:
   
   \[
   PV = \\
],

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You have been offered a job with an unusual bonus structure. As long as you stay with the firm, you will get an extra $68,000 every 7 years, starting 7 years from now. What is the present value of this incentive if you plan to work for the company for 42 years and the interest rate is 5% EAR? (Note: Be careful not to round any intermediate steps less than six decimal places.)

Calculate the present value of receiving a $68,000 bonus every 7 years for 42 years at an interest rate of 5% EAR. This problem involves key concepts such as discounting future payments and applying the present value formula. Follow a step-by-step solution with detailed calculations, ideal for finance and economics students.

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