Accounts & Finance

"a) To calculate the present value of your future pension payments, we need to discount each future payment back to its present value using the given discount rate of 8%. The formula to calculate the present value of a future payment is:

PV = FV / (1 + r)^n

Where:

PV is the present value of the payment.

FV is the future value of the payment.

r is the discount rate.

n is the number of years in the future the payment will be received.

In your case, the pension payment starts at age 65 and continues until age 100. Since you're currently 50 years old, there are 15 years until you turn 65. The pension will continue for 100 - 65 = 35 years (from age 65 to 100).

Let's calculate the present value of each payment and sum them up:

PV = (Pension at age 65) / (1 + r)^15 + (Pension at age 66) / (1 + r)^16 + ... + (Pension at age 100) / (1 + r)^35

Since the pension payment is $80,000 per year, we can plug in the values:

PV = ($80,000) / (1 + 0.08)^15 + ($80,000) / (1 + 0.08)^16 + ... + ($80,000) / (1 + 0.08)^35

Now we can calculate this expression to find the present value of your future pension payments. Please note that the actual calculations can be complex, so using a financial calculator or spreadsheet software would be helpful for accurate results."