The problems of mixed life insurance and insurance in the case of death are considered in the article. The actuarial present value of life insurance is found by solving a system of diаerential equations. The cases of both constant eаective interest rates and variables, depending on the time interval, are examined. The authors used the Pontryagin maximum principle method as the most efficient one, in order to solve the problem of optimal control of the mixed life insurance value. The variable eаective interest rate is considered as the control parameter. Some numerical results were given.