Challenge question. In the chapter text, we dealt exclusively with a single lump sum, but often we may be looking at several lump-sum values simultaneously. Let's consider the retirement plan of a couple. Currently, the couple has four different investments: a $$ 401(\mathrm{k}) $$ plan, two pension plans, and a personal portfolio. The couple is 6 years away from retirement. They believe they have sufficient money in their plans today so that they do not have to contribute to the plans over the next 6 years and will still meet their $$ \$ 1.5 $$ million retirement goal. Here are the current values and growth rates of their plans: $$ 401(\mathrm{k}): \$ 93,000 $$ growing at $$ 6 \% $$. Pension Plan One: $$ \$ 287,000 $$ growing at $$ 6.75 \% $$. Pension Plan Two: $$ \$ 250,000 $$ growing at $$ 7.5 \% $$. Personal Portfolio: $$ \$ 141,000 $$ growing at $$ 10 \% $$. What is the value of the Personal Portfolio 6 years from now?

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To determine the future value of the Personal Portfolio 6 years from now, we can use the **Future Value (FV)** formula for compound interest:

$$
FV = PV \times (1 + r)^n
$$

Where:
- $$ PV $$ = Present Value (\$141,000)
- $$ r $$ = Annual growth rate (10% or 0.10)
- $$ n $$ = Number of years (6)

Plugging in the numbers:

$$
FV = 141{,}000 \times (1 + 0.10)^6
$$

First, calculate $$ (1 + 0.10)^6 $$:

$$
(1.10)^6 = 1.771561
$$

Now, multiply this by the present value:

$$
FV = 141{,}000 \times 1.771561 \approx 249{,}790
$$

**Therefore, the value of the Personal Portfolio 6 years from now is approximately \$249,790.**
The Personal Portfolio will be worth approximately \$249,790 six years from now.

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