Final answer:
The couple had a Joint Life annuity, which provides payments until one of the spouses dies, at which point the payments stop. This is in contrast to Joint and Survivor annuities, where payments continue to the surviving spouse.
Step-by-step explanation:
The type of annuity the couple bought, where payments cease upon the death of one spouse, is known as a Joint Life annuity. This type of annuity is structured to provide payments for as long as either the husband or the wife is alive; however, when one spouse passes away, the payments stop entirely. Unlike Joint and Survivor Annuities, which continue to provide income to the surviving spouse after the first spouse's death, Joint Life annuities do not offer such a feature. These financial instruments are a part of retirement planning and can be influenced by factors like inflation and fixed income, which, even at low rates, can significantly reduce purchasing power over time, a consideration important for those relying on defined benefits plans.