TVM question - Can when to take social security be calculated as a PV of an annuity?


I am trying to apply in the real world what I’ve learned from TVM chapter. I wanted to figure out what formula I could use to determine whether or not to take social security at 66, or wait until 70 years old. If taken at 66 with $1268 monthly payments and invested at a given annual rate of 2% is better than if taken at age 70 with monthly payments of $1968 and also invested at a given annual rate of 2%? Should this be calculated as a perpetuity? or should I use an arbitrary number of years to just get an understanding of what the better option is?

Thank you for any help


How long are you gonna live? If you have an assumption on this, you can simply calculate the future value (FV) at the time of your death and the corresponding present value (PV) today of both scenarios. In general, the longer you live, the better option 2. there will be a “break even age” between option one and two. Regards, Oscar