The correct answer is: A. extended life.
An annuity with an extended life is an annuity that continues to pay out after the original term has expired. This type of annuity is often used to provide income in retirement or to cover long-term care expenses.
A perpetuity is an annuity that pays out an equal amount of money forever. A deferred perpetuity is a perpetuity that does not begin paying out until a certain date in the future. A due perpetuity is a perpetuity that begins paying out immediately.
In conclusion, an annuity with an extended life is classified as an extended life annuity. This type of annuity is an annuity that continues to pay out after the original term has expired.