One of my favorite verses in all of scripture gives me that assurance.
10 And behold, he shall be born of Mary, at Jerusalem which is the land of our forefathers, she being a virgin, a precious and chosen vessel, who shall be overshadowed and conceive by the power of the Holy Ghost, and bring forth a son, yea, even the Son of God.
11 And he shall go forth, suffering pains and afflictions and temptations of every kind; and this that the word might be fulfilled which saith he will take upon him the pains and the sicknesses of his people.
12 And he will take upon him death, that he may loose the bands of death which bind his people; and he will take upon him their infirmities, that his bowels may be filled with mercy, according to the flesh, that he may know according to the flesh how to succor his people according to their infirmities. (Book of Mormon, Alma 7:10-12)