NEED HELP ASAP

Question

Which retirement option is more favorable to you if you retire at age 65? Which retirement option is more favorable to you if you retire at age 55?
At age 18 you start to work for a company and are offered two rather fanciful retirement options.

RETIREMENT OPTION 1: When you retire, you will be paid a lump sum of $15,000 for each year of service.

RETIREMENT OPTION 2: When you start to work, the company will deposit $10,000 into an account that pays 9.6% interest compounded monthly. When you retire the account will be closed and the balance given to you.

Answer 1

If you retire at age 55, you work for 55 - 18 = 37 years.  If you retire at 65, you work for 65 - 18 = 47 years.

 

OPTION 1:  Age 55: (37 years)*($15,000 per year) = $555,000

  Age 65 = (47 years)*($15,000 per year) = $705,000

 

OPTION 2:  Use the compound interest formula, A = P(1 + r/n)^nt

• A = the final amount
• P = the initial investment = $10,000
• r = the annual interest rate expressed as a decimal = 9.6% = 0.096
• n = the number of compoundings per year = monthly = 12
• t = years

 

Age 55:

A = $10,000*(1 + 0.096/12)^12*37

A = $10,000*(1.008)⁴⁴⁴

A = $10,000*(34.4)

A = $344,000

 

Age 65:

A = $10,000*(1 + 0.096/12)^12*47
A = $10,000*(1.008)⁵⁶⁴
A = $10,000*(89.5)
A = $895,000

 

Which option would you pick at age 55?  at age 65?