# Homework 6

Bob and Lisa are both married, working adults. They both plan for retirement and consider the \$2,000 annual contribution a must.

First, consider Lisa’s savings. She began working at age 20 and began making an annual contribution of \$2,000 at the first of the year beginning with her first year. She makes 13 contributions. She worked until she was 32 and then left full time work to have children and be a stay at home mom. She left her IRA invested and plans to begin drawing from her IRA when she is 65. Bob started his IRA at age 32. The first 12 years of his working career, he used his discretionary income to buy a home, upgrade the family cars, take vacations, and pursue his golfing hobby. At age 32, he made his first \$2,000 contribution to an IRA, and contributed \$2,000 every year up until age 65, a total of 33 years / contributions. He plans to retire at age 65 and make withdrawals from his IRA.

Both IRA accounts grow at a 7% annual rate. Do not consider any tax effects.

From the ages of 20 to 32, Lisa contributes \$26,000, \$2,000 over 13 years, to her IRA before she stopped working. Compounding it at 7% annual rate, it equals, \$40,281.29 (2000 * ((1.07) ^ 13-1)/ 0.7 = 40,281.29). Leaving that amount over the next 32 years letting it compound at the same rate by the age of 65, Lisa will have \$351,062.35 (40,281.29 * (1.07 ^32) = \$351,062.35). Bob on the other hand won’t have nearly as much. Starting his contribution at age 32, Bob contributes the same amount as Lisa, however over a shorter period; Lisa has a total of 45 years invested versus Bob’s 33 years. By 65 Bob will only have \$237,866.85 (2000 * ((1.07) ^ 33-1) / 0.07 = 237,866.85).

This scenario demonstrates the importance of saving and investing early. Although Bob and Lisa invested the same amount of money, Lisa’s investment was able to mature longer than Bob’s was. Although Bob’s total number contributions exceeds Lisa’s, he still comes up about 38% short of what Lisa made.

 Lisa Bob Age investment initiated 20 32 Starting Balance 0 0 Annual Contribution \$2,000 (Until the 32) \$2,000 Age of Retirement 65 65 Rate of Return 7% 7% # of Years (contributions) 45 33 Total Contributions \$26,000 \$66,000 Balance at Retirement \$351,062.35 \$237,866.85

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