The actuarial present value of the N-year final annuity is equal to the actuarial present value of the 100-year (equivalent to life) final annuity minus the actuarial present value of the N-year final annuity converted to zero.

The actuarial present value of life-long termination annuity is equal to the actuarial present value of N-year termination annuity plus the actuarial present value of N-year termination annuity converted to zero.

If you still don't understand, you can ask me I majored in insurance and passed the actuarial exam A2 Financial Mathematics.