Suppose your retirement account has a balance today of $25,000 and you are 20 years old. If you are invested in a diversified portfolio of stocks, you might hope that the historical return of about 6% continues into the future. Consider how the balance in your retirement account evolves as you age under the different assumptions below. (If you like, use a spreadsheet program to help you with this question.)
(a) Compute the balance in your retirement account when you will be 25, 30, 40, 50, and 65 years old assuming the average annual rate of return is 6%. Assume there are no deposits or withdrawals in this account, so the original balance just accumulates.
(b) Do the same thing for rate of return of 5% and 7%. How sensitive is the calculation to the rate of return?
(c) Plot your retirement account balance for these three scenarios (6%, 5%, 7%) on a standard scale.
(d) Do the same thing with a ratio scale.