Yes, it totally makes sense to buy term insurance even after 60 years of age. In case, your children or grandchildren are studying and are financially dependent on you. Also, if you have a spouse who is dependent on your pension, which would stop after your demise, term insurance is helpful. Or in case you have some financial outstandings to repay such as a home loan or any other debt, term insurance can be used to pay off the same in case of your unfortunate death.