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

Answer:

• The reduction is 8.6%

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

• $Pension=F(1+0.06/12)^{12\times 3.5}=1.233F$

For retirement at 67:

• t = 67 - 62 = 5

• $Pension=F(1+0.06/12)^{12\times 5}=1.349F$

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

• $(1.349F-1.233F)\times 100/(1.349F)=8.6\%$