Part 2: Solution
Let's see how well you answered the questions.
| 1. |
Help Maria's parents by developing the following chart. This chart will give them a sense of the alternatives they face and the expected results of the investment strategy they will eventually adopt. Calculate the expected value of the retirement fund for 10, 12, and 15 years for each of the three strategies (i.e., investing in CDs, AAA bonds, and stocks). Use your answers to fill in the chart below and then check your solutions by clicking on "How did I do?" |
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Your Answer: |
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Future Value Retirement Fund
$80,000 Initial Value, $250 Contribution at the end of Each Month |
| Investment |
Expected Return |
10 Years |
12 Years |
15 Years |
| CDs |
6% |
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| AAA |
8% |
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| Stocks |
12% |
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Our Answer: |
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All three alternatives are solved as a combination of the future value of an ordinary annuity (the $250 monthly payment stream) and the future value of a single cash flow (finding the value of the current $80,000 nest egg). The interest rates, must be converted to monthly rates for the annuity solutions by dividing them by 12, while the number of years must be multiplied by 12 to account for the monthly payment periods. The solutions are given in the following table: |
Future Value Retirement Fund
$80,000 Initial Value, $250 Contribution at the end of Each Month |
| Investment |
Expected Return |
10 Years |
12 Years |
15 Years |
| CDs |
6% |
$186,521 |
$216,598 |
$269,032 |
| AAA |
8% |
$223,308 |
$268,398 |
$351,063 |
| Stocks |
12% |
$321,541 |
$415,015 |
$604,559 |
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| 2. |
What lessons should Maria's parents draw from this chart about the relationship between time, value, and type of investment? |
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Your Answer: |
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Our Answer: |
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The chart shows that the longer one invests, the more the retirement fund will build up. This is illustrated by looking across any row of the chart. For example, investing for 15 years, rather than 10 years, in stocks almost doubles one's savings. In this case, a 50% increase in the time one invests leads to a nearly 100% expected increase in one's savings. The chart also shows the dramatic difference that higher returns make in the ending values. This effect is illustrated by looking down the chart. Moving from CDs (6%) to stocks (12%) adds substantially to one's savings. Last, moving along the chart's diagonal shows the combined effect of investing longer and investing in higher risk securities. Combined, these effects more than triple the expected amount of savings. |
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| 3. |
Now let's see what happens if Maria's parents increase their monthly saving from $250 to $350. Complete the chart below in the same fashion as you did in the first problem, clicking the "How did I do?" button to check you work. |
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Your Answer: |
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Future Value Retirement Fund
$80,000 Initial Value, $350 Contribution at the end of Each Month |
| Investment |
Expected Return |
10 Years |
12 Years |
15 Years |
| CDs |
6% |
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| AAA |
8% |
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| Stocks |
12% |
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Our Answer: |
Future Value Retirement Fund
$80,000 Initial Value, $350 Contribution at the end of Each Month |
| Investment |
Expected Return |
10 Years |
12 Years |
15 Years |
| CDs |
6% |
$202,910 |
$237,613 |
$298,114 |
| AAA |
8% |
$241,602 |
$292,449 |
$385,667 |
| Stocks |
12% |
$344,544 |
$446,921 |
$654,517 |
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| 4. |
In 10 years, the CDs, which return 6%, will produce $186,521 if Maria's parents invest $250 each month, and $202,910 if they invest $350 each month. (Note: This includes the future value of the $80,000 already accumulated by Maria's parents.) Since these are 10-year results, they reflect 120 deposits. This means that with the $350/month strategy, a total of $12,000 more was deposited than with the $250 strategy. Why, then, do the final numbers differ by $16,389 ($202,910 - $186,521)? |
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Your Answer: |
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Our Answer: |
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They differ because more interest is earned on the additional $100 monthly deposit. This extra interest earned each month then earns interest in subsequent months, compounding itself and thereby increasing the benefit of the additional savings strategy. |
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© 2002 by Prentice-Hall, Inc.
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