SOLUTION: 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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 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      Log On


   

Question 1130371: 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?
(b) Which retirement option is more favorable if you retire at age 55?

Please show me how you get the answers, thank you.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
This is the formula for compound interest:

N=P%281%2Br%2Fn%29%5Ent

N is the new amount.
P is the principal amount.
r is the annual interest rate.
n is how often the interest is compounded per year.
t is the number of years.

Option 1:

At age 65 (47 years service): 47 * $15,000 = $705,000

At age 55 (37 years service): 37 * $15,000 = $555,000

--------------------------------------------------------

Option 2:

At age 65 (47 years service):

N=10000%281%2B0.096%2F12%29%5E%2812%2A47%29 = $894,829.12

At age 55 (37 years service):

N=10000%281%2B0.096%2F12%29%5E%2812%2A37%29 = $343,934.91

--------------------------------------------------------

So, at age 65 (47 years service), Option 2 is best. At age 55 (37 years service), Option 1 is best.