Question

A company provides a monthly pension to its employees. A person retiring at 62 retires and receives a full monthly pension. If the person continues to work the pension goes up 6% per year for a maximum of 5 years. Since people don't always retire on their birthday the year is divided into 12th's. If a person retires at 65.5, What is the percent reductions of their pension , compared to what they would receive at 67?

Answer 1

• The reduction is 8.6%

Step-by-step explanation:

Call F the full monthly pension of a person retiring at 62.

If a person continues to work the pension grows at a rate of 6% per year, compounded monthly, so use the compounded growing formula:

• 
  `Pension=F(1+r/12)^(12t)`

Where r = 6 / 100 = 0.06, and t = number of years after retirement.

For retirement at 65.5:

• t = 65.5 - 62 = 3.5

• 
  `Pension=F(1+0.06/12)^(12* 3.5)=1.233F`

For retirement at 67:

• t = 67 - 62 = 5

• 
  `Pension=F(1+0.06/12)^(12* 5)=1.349F`

Percent reduction of people who retire at 65.5 compared to what they would receive at 67:

• 
  `(1.349F-1.233F)* 100/(1.349F)=8.6\%`