Massachusetts Mutual Life Insurance Co. has agreed to pay $1.6 million to settle charges it misled customers about an obscure restriction in $2.5 billion worth of variable annuities sold from 2007 to 2009, federal regulators said Thursday.

The Springfield insurance giant failed to fully explain a feature that capped the benefits for certain optional riders in the annuities, the Securities and Exchange Commission ­alleged. In a worst-case scenario, investors could stop receiving annual income from the investments once the cap on withdrawals was reached.