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Eduardwww [97]
3 years ago
9

A company provides a monthly pension to its employees. A person retiring at 62 retires and receives a full monthly pension. If t

he 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?
Mathematics
1 answer:
IRISSAK [1]3 years ago
8 0

Answer:

  • <em><u>The reduction is 8.6%</u></em>

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.

<u>For retirement at 65.5</u>:

  • t = 65.5 - 62 = 3.5

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

<u>For retirement at 67</u>:

  • t = 67 - 62 = 5

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

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

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