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Amount of the yearly pension payment

Problem: Your salary for the coming year is $100,000 (payable one year from now) and you expect to work for another 30 years. You expect your annual base salary to grow at a 4% annual rate during the remainder of your career. Your company's pension plan calls for you to receive a yearly pension payment after you retire equal to 25% of your final year's base salary. The first payment will be made one year after your retirement, and you expect to live for twenty years after your retirement. The interest rate is 8% per year.

1) What is the amount of the yearly pension payment that you can expect to receive under this plan (assume that you will receive your $100,000 base salary payment one year from now)?

2) Now suppose you are contemplating a switch to a new employer. The new employer will match your annual base salary, and you can expect this to grow at a 4% annual rate until your retirement. However, the new employer offers no pension plan. The new employer offers to pay you a flat annual bonus, on top of your base salary, to compensate you for the loss of the pension plan. How much of an annual bonus would you require before you were just willing to make the switch?

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