Generally, yes. However, where periodic payments are made on account of personal injury or sickness under IRC §104(a)(2), both the payments and the compounded growth or interest are excluded from gross income, and the plaintiff need not pay income tax on them.
For example, in A v. D, 482 A.2d 531 (1984), a minor deformed by drugs administered to his mother during pregnancy received a lump sum payment of $225,000 which was used to purchase an annuity. The court in its opinion noted that if the boy lived to his normal life expectancy that the payments would total over $3,000,000, yet nevertheless held that the entire amount was excludable—and he need not pay income tax on them.