Question 1130840: At the age 18 you start to work for a company and are offered two rather fanciful retirement options.
Retirement 1 option: When you retire, you will be paid a lump sum of $15,000 for each year of service
Retirement 2 option: 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 is given to you.
(a) Which retirement option is more favorable if you retire at age 65
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
(I will assume this post is from the same person who submitted the same question for a worker who retires at 55...)
Option 1: $15000 a year for 47 years: 
Option 2: $10000, multiplied by 1.008 (1 plus the monthly interest rate) for (12*47) months: 
For working 47 years, the single deposit earning compound interest is substantially higher.
Comparing the two problems with the different numbers of years of service, you can see that the amount from Option 1 is a linear relationship with the number of years, whereas the amount from Option 2 grows exponentially. Because of the smaller initial investment amount, Option 1 is still better for 37 years of service; the exponential growth of Option 2 hasn't quite caught up with the linear growth from Option 1. But by 47 years of service the amount from Option 2 with is exponential growth has far surpassed the linear growth of Option 1.
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comment from student:
Now I'm confused with your numbers. So option 1 would be 15,000 for 65 years instead of 47? How did you get 1.008?
(1) Option 1 is $15000 for each year the employee worked for the company. Starting at age 18 and working until age 65 is 47 years.
(2) The annual percentage rate for Option 2 is 9.6% = 0.096. The monthly interest rate is 1/12 of that: 0.008. The monthly GROWTH FACTOR is 1+.008 = 1.008.
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