Mr. P was born between 1943 and 1954, so his full retirement age for social security monthly payments is age 66.
However, he can begin receiving a reduced monthly benefit at age 62. The monthly retirement benefit is reduced by 25% and he
would continue to receive that reduced amount for the rest of his life.
Mr. P wants to know what age he would be (year and month) when the total amount of the reduced monthly benefits
from age 62 to this age would equal the total of all the full monthly benefits from age 66 to this age.
Please give your answer in years and months (for example, 67 years 2 months).
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.
Correctly solved by:
| 1. David & Judy Dixon | Bennettsville, South Carolina |
| 2. K. Sengupta | Calcutta, INDIA |
| 3. Richard K. Johnson | La Jolla, California |