Question

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 effect. Write a two to three (2-3) paragraph summary in which you: Create a chart summarizing the details of the investment for both Bob and Lisa. Explain the results in terms of time value of money.

Answer 1

Lisa has made 13 contributions of $2,000 till the age of 32.

Her total contribution is $2000*13 = $26,000

Her Age of retirement is 65. So No. of contributions is 45

Therefore her balance at retirement will be :

At age 32- $2000 * ((1.07) ^ 13-1)/ 0.7 = 40281.29

At age 65-  $40,281.29 * (1.07 ^33) = $375,636.72

She started drawing from her IRA from the age 65

Her amount till the age of 65 would be: $40,281.29 * (1.07 ^33) = $375,636.72

Bob has made 33 contributions of $2,000 till the age of 65.

His total contribution is $2000*33 = $66,000

His age of retirement is 65. So No. of contributions is 33

Therefore his balance at retirement will be :

$2000 * ((1.07) ^ 33-1) / 0.07 = $237,866.85

	LISA	BOB
Investment age	20	32
Contibution per year	$2,000	$2,000
Retirement Age	65	65
No. of years till maturity	45	33
Total contribution	$26,000	$66,000
Return Rate	7%	7%
Balance at Retirement	$375,636.72	$237,866.85

By analysing the investment plan of both Bob and Lisa we can say that the balance at retirement of Lisa is more than the balance at retirement of Bob .This is because she began to save early at the age of 21 and continued investing till the age of 32 whereas Bob started saving at the age of 32 and continued investing until the age of 65, this means Lisa has invested for a longer period of time which helped her to grow the annuity amount.

This shows that inspite of investing less amount of contribution ,her balance at retirement was $ 137770.18 more than the bob Hence we can conclude that the length of time of the investment is much more important than the size of the contribution.