Solution to the Problem:
The answer is at age 78 years, 0 months.
At that age, the total of all the reduced monthly benefits will equal the total of all the full monthly benefits.
Let x = Full monthly benefit.
Let n = number of months from age 66 until the two totals are equal.
Then the reduced monthly benefit is .75x.
There are 4 years or 48 months between age 62 and age 66, and if he retired at age 62,
he would be getting the reduced rate for that many months.
So, 48(.75x) + n (.75x) = nx
Solving this equation, x will divide out, and you obtain n = 144 months.
So, the two totals will be equal in 144 months from age 66.
Since 144 months = 12 years, the age that Mr. P is looking for is 78 years 0 months.